The main purpose of this study is to see if taking dupilumab is effective in treating Eosinophilic Esophogitis (EoE). The study will determine if dupilumab is an effective treatment compared with placebo in adult and adolescent patients. Dupilumab is administered through a subcutaneous injection (shot). Dupilumab is is an investigational drug, which means that it is not yet approved to treat EoE. Participation in the study will last up to 48 weeks.