How can I tell if a teenage girl has a eating disorder?

You may not be able. To tell! if you suspect it, try to have her evaluated by a psychiatrist with experience in eating disorders.
See below. Anorexia is easier to observe as the teen will continue to lose weight and your attempts to provide nutrition will meet with resistance. Bulimia can be difficult to detect as teens with this illness are very guarded about it. Friends who want the teen to be healthy are a good resource.