You don't need a low carb diet to lose fat. But you can't expect to starve yourself, not exercise and still lose bodyfat. Your goal of losing 10-15lbs of fat should be fairly easy to accomplish if you stick with a diet and workout program for 8-12 weeks. Add weight training in there and you'll look like a new person. Before you go, just one more "sample diet" you can follow and make adjustments:
Meal1: 1/2 cup oats, 4 egg whites, or egg substitue 1Tbs Olive Oil
Meal 2: 1/2 cup cottage cheese , 2 Tbs. Natural Peanut Butter
Meal 3: Tuna in Olive Oil on 2 Slice Whole Wheat bread (If 1/2 cup brown rice is not possible)
Meal 4: Protein Shake with Udo's Choice or any other healthy oil, Any "healthy" snack that you like to break up the monotony of the diet.
Meal 5: 8oz. chicken, turkey, lean ground beef, flank steak, fish..., 1/2 cup brown rice, steamed veggies.
Meal 6: 1/2 cup cottage cheese, 1 Tbs. Natural Peanut Butter or Another protein shake or carb/protein meal of your choice.