Sit her down and tell her she's beautiful and brilliant. Then take her downstairs to the French restaurant and buy her a plate of Filet Mignon. Then take her to the ice cream shop next door and buy her a hot fudge sundae. Then take her back upstairs and use a hammer and nails to seal the bathroom door and the front door shut so she can't get out and she can't go to the bathroom to vomit or defecate. You're going to have to stay up with her for the next 48 hours while she kicks her habit. Once her first meal is digested, make her eat some pancakes or some mashed potatoes. Just keep her belly full and force her to digest everything. There's going to be a lot of name-calling. For example, if you're divorced, she'll probably say things like "No wonder mommy/daddy left you" or "What's a matter? Lonely now that you don't have a spouse? Is that why I have to be locked in here with you, you fucking disgusting can't-keep-a-spouse-in-the-house divorcee." That's the addiction to vomiting/defecating talking. It's not your daughter. Try to let it slide.
After the 48 hours are up, you'll have your daughter back. No more cutting herself. No more dried up corners of the mouth. Just your beautiful daughter who will finally know that she doesn't need to vomit and defecate a lot to be pretty. You're a good parent and, if some of the things your daughter is going to say are true, you're a terrible spouse and shouldn't remarry.
Happy Your Teenage Daughter Is Bulimic Day!