Losing fat while building muscle: is this possible?

Goal weight (in terms of losing the fat I need to lose, not the muscle I hope to gain) is approximately 210 lbs. I would like to put on between 10 and 15 pounds of muscle – already a well-built guy but in the process of losing weight (highest was 407) I have lost a fair amount of muscle mass. Definition is not a priority, though my goal is not hulk-like strength or bulk, but rather solid, lean, healthy (and noticeable, I suppose) muscle mass. I understand the inherent contradiction in my question (trying to lose weight while gaining weight), but I find it hard to believe that – as I have read on countless sites – I cannot simultaneously lose fat and gain muscle as losing fat requires a decrease in caloric intake and gaining muscle requires an increase. Anyone have any suggestions? All comments and answers are welcomed and appreciated.

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