I consider the two-body decay of a particle at a hadron collider into a visible and an invisible particle, generalizing W -> ev, where the masses of the decaying particle and the invisible decay particle are, a priori, unknown. I prove that the transverse mass, when maximized over possible kinematic configurations, can be used to determine both of the unknown masses. I argue that the proof can be generalized to cover cases such as decays of pair-produced superpartners to the lightest, stable superpartner at the Large Hadron Collider.