I think you need to ask the question in another way. Are you trying to lose weight or are you trying to lose fat? To lose fat you need to do two things: 1. Stop gaining fat from your diet and , 2. Burn the fat that is there. To do two you need to use it as a source of fuel for energy. You might be better using cold to do that to be frank!

Weight loss is pretty darn simple. If calories used is greater than calories taken in by eating you lose weight. I you reduce the intake but that is still more than what's used from a sedentary life then you still won't lose weight. You just won't gain as much as you would have. Low intensity, long duration exercise is required to burn fat. You might need to build into that. But as you exercise don't think you can increase the food intake. To do that is counter productive. You are trying to increase the calories used without increase the calories ingested.