If I'm maintaining at my current calories, can't I just add exercise to burn off the fat I want to lose?

There are two main types of fat. Visceral surrounds your organs, and subcutaneous is beneath the skin. You need to lose both types. While exercise is excellent for burning subcutaneous fat, it is nutrition management that seems to have the greatest impact on visceral fat. Therefore, the combination of reducing calories via nutrition and increasing exercise has been shown to be the optimal combination.

Understand that this is all relative. If you are eating clean and add exercise, you are probably creating the nutrition deficit because the nutrient dense foods will raise your metabolism. If you are eating sloppy and adding exercise, then expect to perhaps drop a few pounds to appear "skinny-fat" and still enjoy the myriad of health issues that come from poor diet (number two cause of preventable death in the U.S. in 2000).