Erlotinib in Combination With Temozolomide in Treating Relapsed/Recurrent/Refractory Pediatric Solid Tumors

Inclusion Criteria: * One to 21 years of age * Relapsed, recurrent, or refractory malignancy. All solid tumor diagnoses will be eligible. * Pathologic confirmation of the diagnosis either at original diagnosis or recurrence. * Known non-synonymous mutation in the following genes: EGFR, ERBB2, or JAK2V617F (JAK2). Genomic sample preferably from relapse, but may be from other stage of treatment if relapse sample is not reasonably obtainable. Genetic analysis for determination of eligibility occurs as part of routine care and is not being performed specifically for the purposes of this study. * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT or MRI scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam. * Prior therapy as follows: * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study. * Myelosuppressive chemotherapy: Patients must not have received myelosuppressive chemotherapy within 2 weeks of enrollment onto this study (6 weeks if prior nitrosourea). * Hematopoietic growth factors: At least 14 days must have elapsed after receiving pegfilgrastim and least 7 days must have elapsed since the completion of therapy with a non-pegylated growth factor. * Biologic (anti-neoplastic agent): At least 7 days must have elapsed since completion of therapy with a biologic agent. For agents that have known adverse events occurring beyond 7 days after administration, this period prior to enrollment must be extended beyond the time during which adverse events are known to occur. * Monoclonal antibodies: At least 3 half-lives must have elapsed since prior therapy that included a monoclonal antibody. (See posting of half-lives for commonly used monoclonal antibodies on the DVL homepage; https://members.childrensoncologygroup.org/Disc/devtherapeutics/default.asp.) * Radiotherapy: At least 2 weeks must have elapsed since local palliative XRT (small port); at least 6 weeks must have elapsed since treatment with therapeutic doses of MIBG; at least 3 months must have elapsed if prior craniospinal XRT was received, if more than 50% of the pelvis was irradiated, or if TBI was received; at least 6 weeks must have elapsed if other substantial bone marrow irradiation was given. * Stem cell transplant or rescue without TBI: No evidence of active graft vs. host disease and at least 2 months must have elapsed since transplant. * Patients must have a performance status corresponding to Karnofsky or Lansky greater than or equal to 50%. Use Karnofsky for patients \> 16 years of age and Lansky for patients ≤ 16 years of age. Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. * Normal bone marrow and organ function as defined below: * Absolute neutrophil count ≥ 1,000/mcl * Platelets ≥ 100,000/mcl * Total bilirubin ≤ 1.5 x IULN * AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN * Creatinine ≤ IULN OR creatinine clearance ≥ 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * INR ≤ IULN or PT ≤ IULN * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * A history of other malignancy ≤ 5 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix. * Currently receiving any other investigational agents. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to erlotinib, temozolomide, or dacarbazine. * Currently on the following concomitant medications or substances that have the potential to affect the activity or pharmacokinetics of the study drug(s). The use of the following medications should be discontinued prior to initiation of protocol therapy and should be avoided during protocol therapy if reasonable alternatives exist. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, renal failure, cardiac arrhythmia, interstitial lung disease, hepatic failure / hepatorenal syndrome, GI perforation, cerebrovascular event, microangiopathic hemolytic anemia, corneal perforation/ulceration, or documented Hepatitis B virus infection. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative serum or urine pregnancy test within 7 days of study entry. * Known HIV-positivity on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with erlotinib or temozolomide. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.