How do I lose 20 pounds the right way?

I'm a 16 year old girl and I've always been on the heavy side. I'm not fat or obese but I don't look the way I would like to (but what 16 year old girl likes the way they look?). Right now I weigh 160 and I'm 5'7" with a medium-large frame. I would like to be around 140. I want to lose it in a healthy way and keep it off so if it takes longer than 2 months I'm ok with that, but 2 months would be ideal. I've struggled with eating disorders in the past so I would really like to stay away from serious dieting--maybe just cutting out a few foods but nothing too big. I don't want to fall back into my old habits; I've worked hard over the past few years to look at food without hatred. I don't exactly know how to lose weight in a healthy way and keep it off... will exercising 2-3 times a week and cutting out junk food be enough?