The effect of reducing calorie intake is so much greater than exercising more. If you could reduce your calories by 500/day that would be like working out vigorously for 1 hour every day. Its all just inputs and outputs. If your baseline calorie burn assuming no exercise is 1500/day and you reduce from 1750 to 1250, then over time you will lose weight.

In either case, the mechanism is the same, you convert organic carbon compounds to CO2 and water and excreting those through breathing and urination is how the weight goes from your body back to the environment.