Can I gain muscle without gaining much fat?

I'm 18 and somewhat underweight because I was formerly anorexic. I'm on the road to recovery and I hope to gain about 10 pounds, which will put me at a normal BMI. Since all my muscles atrophied, I'm more determined to gain muscle m rather than fat. If I go on a high-protein, low-cal, low-fat, low-carb diet and exercise a lot, is it possible to gain lots of muscle and little fat?