This paper presents an application of the Electro-magnetic Time Reversal (EMTR) in changing media to identify the fault location along a single-conductor transmission line. It is shown that the time-reversed quantities exhibit a property, called Mirrored Minimum Energy, that permits the identification of the fault location along the line. Specifically, the fault location can be determined by analyzing the energy of voltage signal along the modified propagation medium with only one simulation run. As a consequence, the efficiency of the conventional EMTR-based fault location techniques is significantly improved. The observed property is introduced in the frequency domain by taking advantage of the transmission-line equations, and further validated by means of numerical simulations and a reduced-scale experiment.