The primary objective of the study is to investigate the efficacy of Atomoxetine (ATMX) in the treatments of adolescent and young adult Attention Deficit Hyperactivity Disorder (ADHD) with comorbid Substance Use Disorder (SUD). The secondary objective of the study is to determine the efficacy of ATMX in preventing SUD relapse. As previous pre-clinical work has demonstrated that ATMX has led to significant improvement in ADHD in children and lacks abuse liability, the investigators hypothesize that ATMX will be efficacious in treating ADHD in adolescents and young adults with SUD, and that ATMX will also be efficacious in preventing SUD relapse.