That is called "Differential Time Of Arrival" (DTOA). And the localization method is called trilateration, not triangulation. Helps with googling if you get your terms right.
We did a robot localization system using three beacons around the area and one in the robot. The robot sent a pulse and the beacons responded to that. The robot could localize itself by listening the responses. You would need three microphones (or beacons) to locate the sound source on a plane. With two microphones you get a line (hyperbola) where the sound source might be. If you want I can post the math for intersection of two hyperbolas.. If I find my notes. The solution comes down to few (~10) multiplications and divisions (~2) and finally solving an intersection of two lines.