Must agree here. Lose weight than gain muscle.

If it is possible to do both? Yes it is. Is it harder ... oh yeah very much harder. Slower? Possibly

What i would do if i wore you, is to figure out how much kcal i need to maintain the same weight.

Then i would lower on Carbs , and increase on protein and healthy fat (just a bit here, this will decrease your starvation)

Less carbs will lead you to use or storage energy (fat), more protein will give you fuel for the muscle (do put too much, or it can turn to fat), healthy fat is needed, and gives you the feel you eat enough.

do a weekly checkup on your weight and measures, if you see it's not working change your diet.