Will running two miles per day on a standard 1800 calorie diet help me burn body fat and gain muscle?

Yes and no. In men and women, resistance training combined with a healthy diet will build muscles....More in men than women but it works for both. Stronger muscles tend to burn more calories than weaker muscles even when you are not using them...That helps reduce fat. Lifting with proper form to the point of momentary failure plus a good diet seems to be the best way to get the muscles to respond.