A Study to Evaluate the Efficacy and Safety of E2086 in Adults With Narcolepsy

Inclusion Criteria: Participants must meet all of the following criteria to be included in this study: 1. Male or female, age greater than or equal to (\>=) 18 years (or as regionally appropriate) at the time of informed consent 2. NT1 Cohort: Must fulfill Inclusion Criteria 2a and 2b 1. Diagnosis of NT1 within the last 10 years of screening, as confirmed by at least one of the following: * Polysomnography (PSG) and Multiple Sleep Latency Test (MSLT) results, and clinical history, consistent with the 2023 International Classification of Sleep Disorders, 3rd edition, text revision (ICSD-3-TR) criteria for NT1 * Cerebrospinal fluid orexin-A/hypocretin-1 concentration less than or equal to (\<=) 110 picograms per milliliter (pg/mL) 2. At least 4 or more episodes of cataplexy/week as averaged over 2 weeks minimum and confirmed by the cataplexy portion of the Diary If PSG or MSLT results are not available within the last 10 years of screening to fulfill Criterion 2a then screening assessment results for PSG or MSLT can be used instead 3. NT2 Cohort: Diagnosis of NT2 within the last 10 years of screening, as confirmed by PSG and MSLT results, and clinical history, consistent with the 2023 ICSD-3-TR criteria for NT2 If PSG or MSLT results are not available within the last 10 years of screening to fulfill Criterion 3 then screening assessment results for PSG or MSLT can be used instead 4. ESS score \>=10 5. Reports regular bedtime, defined as the time that the participant attempts to sleep, between 22:00 and 01:00 (based on data from the screening Diary) 6. Reports regular waketime, defined at the time the participant gets out of bed for the day, between 05:00 and 10:00 (based on data from the screening Diary) 7. Reports being in bed between 7 and 9 hours per night (based on data from the sleep portion of the Diary) 8. Compliance rate \>=80 percentage (%) for completion of the Diary during screening 9. Body mass index (BMI) \>=18 to less than (\<) 35 kilograms per square meter (kg/m\^2) at Screening Exclusion Criteria: 1. Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta-human chorionic gonadotropin \[ß-hCG\] (or human chorionic gonadotropin \[hCG\]) test with a minimum sensitivity of 25 international units per liter (IU/L) or equivalent units of ß-hCG \[or hCG\]). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 72 hours before the first dose of study drug 2. Females of childbearing potential who: * Within 28 days before study entry, did not use a highly effective method of contraception, which includes any of the following: 1. total abstinence (if it is their preferred and usual lifestyle) 2. an intrauterine device or intrauterine hormone-releasing system (IUS) 3. a contraceptive implant 4. Combined estrogen and progestogen-containing hormonal contraception (oral, intravaginal, transdermal) or progestogen-only hormonal contraception associated with inhibition of ovulation, such as desogestrel (oral, injectable). Participants using hormonal contraceptives must be on a stable dose of the same contraceptive product for at least 28 days before dosing, throughout the study and for at least 28 days following study drug discontinuation 5. have a vasectomized partner with confirmed azoospermia * Do not agree to use a highly effective method of contraception (as described above) throughout the entire study period and for 28 days after study drug discontinuation. Participants on an oral contraceptive must use an additional study method throughout the study and for 28 days after study drug discontinuation. For sites outside of Europe, it is permissible that if a highly effective method of contraception is not appropriate or acceptable to the participant, then the participant must agree to use a medically acceptable method of contraception, that is, double-barrier methods of contraception such as latex or synthetic condom plus diaphragm or cervical/vault cap with spermicide. NOTE: All females will be considered to be of childbearing potential unless they are postmenopausal (amenorrheic for at least 12 consecutive months, in the appropriate age group, and without other known or suspected cause) or have been sterilized surgically (that is, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing). 3. Clinically significant illness that requires medical treatment within 8 weeks of dosing or a clinically significant infection that requires medical treatment within 4 weeks of dosing 4. Evidence of disease that may influence the outcome of the study within 4 weeks before dosing (for example, psychiatric disorders and disorders of the gastrointestinal tract, liver, kidney, respiratory system, endocrine system, hematological system, neurological system, or cardiovascular system) 5. Any history of surgery that may affect PK profiles of E2086 (for example, hepatectomy, nephrectomy, digestive organ resection) or who have a congenital abnormality in metabolism at Screening 6. Any clinically abnormal symptom or organ impairment found by medical history at Screening, including severe renal impairment (estimated glomerular filtration rate \[eGFR\] \<30 milliliters per minute (mL/min), and physical examinations, vital signs, ECG findings, or laboratory test results that require medical treatment at Screening or Baseline 7. A prolonged QTc interval calculated using Fridericia's formula (QTcF) greater than 450 milliseconds (ms) according to central reading at Screening or Baseline. If the QTcF machine read is greater than 450 ms on the first single 12-lead ECG, 2 additional 12-lead ECGs will be performed 1 minute apart and the mean of the 3 QTcF values will be calculated 8. Persistent systolic BP greater than (\>) 130 or \<100 millimeters of mercury (mmHg) or diastolic BP \>85 or \<50 mmHg at Screening (based on BP measured on at least 3 occasions over 2 weeks), or at Baseline. If outside of these limits at Screening or Baseline, BP should be repeated twice with at least 5 minutes between measurements 9. Persistent HR less than 50 beats/min or more than 100 beats/min at Screening (based on HR measured on at least 3 occasions over 2 weeks), or at Baseline. If outside of these limits at Screening or Baseline, HR should be repeated twice with at least 5 minutes between measurements 10. Any lifetime history of suicidal behavior as indicated by the C-SSRS 11. Current unstable psychiatric disorder, current active major depressive episode or an active major depressive episode in the past 6 months 12. Any suicidal ideation with intent with or without a plan at Screening or within 6 months of Screening (that is, answering "Yes" to questions 4 or 5 on the Suicidal Ideation section of the C-SSRS) 13. Psychotic disorder(s) or unstable recurrent affective disorder(s) evident by use of antipsychotics within 2 years before Screening 14. Hypersensitivity to the study drug or any of the excipients 15. Intake of herbal preparations containing St. John's Wort within 5x the half-life before dosing 16. Any history of or concomitant medical condition that in the opinion of the investigator(s) would compromise the participant's ability to safely complete the study 17. Planned surgery that requires general, spinal, or epidural anesthesia that would take place during the study. Planned surgery which requires only local anesthesia and that can be undertaken as a day case without inpatient stay postoperatively need not result in exclusion if in the opinion of the investigator this operation does not interfere with study procedures and participant safety 18. Known to be human immunodeficiency virus (HIV) positive 19. Acute Epstein Barr virus (EBV) infection with a positive EBV Viral Capsid Antigen Antibody (VCA) IgM at Baseline 20. Known to be hepatitis B virus (HBV)-positive with a detectable HBV (for example, hepatitis B surface antigen \[HBsAg\] reactive) within 6 months before the 1st dose of study drug, or hepatitis C virus (HCV) positive with a detectable (for example, HCV ribonucleic acid (RNA) \[qualitative\]) viral load. Note: Participants who are HCV positive due to prior resolved disease can be enrolled, only if a confirmatory negative HCV RNA test is obtained and the participant has completed active treatment 21. Initiation of statin therapy, or a change to a different statin, or an increase in the dose of a statin within the 6 months before the planned start of study drug 22. History of formally diagnosed moderate to severe obstructive sleep apnea (OSA) 23. Current use of continuous positive airway pressure (CPAP), hypoglossal nerve stimulator, oral device, or other therapy for the treatment of OSA 24. Symptomatic restless legs syndrome 25. Apnea-hypopnea index \>=15 on Screening PSG 26. Use of anticataplectic medications (including but not limited to antidepressants) within 5× the half-life before Screening 27. Use of psychostimulant medications, prescription and over-the-counter (OTC), within 5× the half-life before Screening until after the Follow-Up Visit. Examples of prohibited medications include OTC stimulants (for example, pseudoephedrine), methylphenidate, amphetamines, modafinil, armodafinil, sodium oxybate, pitolisant, solriamfetol, and pemoline 28. Use of sleep promoting or sedating medications, prescription and OTC, within 5x the half-life before Screening until after the Follow-Up Visit. Examples of prohibited medication include OTC sleep aids, trazodone, hypnotics, benzodiazepines, barbiturates,cannabinoids, melatonin, melatonin receptor agonists, dual orexin receptor antagonists, and opioids 29. Inability to discontinue use of strong (such as antifungal itraconazole and antibiotic clarithromycin) and moderate (such as antifungal fluconazole) Cytochrome P450 3A (CYP) 3A inhibitors within 5x the half-life before dosing until after the Follow-Up Visit 30. Inability to discontinue use of CYP3A inducers (such as antibiotic rifampicin and anti-convulsant phenytoin) within 5x the half-life before dosing until after the Follow-Up Visit 31. History of drug or alcohol dependency or abuse within 2 years before Screening, or those who have a positive urine drug test or breath (or urine) alcohol test at Screening or Baseline 32. Does not agree to abstain from use of recreational drugs during the study 33. Currently enrolled in another clinical study or used any investigational drug or device within 28 days or 5x the half-life, whichever is longer, preceding informed consent 34. Receipt of blood products within 4 weeks of dosing, donation of blood within 8 weeks of dosing, or donation of plasma within 1 week of dosing 35. Past participation in a study of an orexin agonist if discontinuation of orexin agonist use was related to an adverse drug reaction or inefficacy