This paper examines the exploration of a weighted graph by two mobile agents, where the energy cost of traversing an edge is equal to the edge weight. Agents located at the same position (potentially on an edge) can freely transfer energy, but one agent may unpredictably crash and cease operation. Two settings are considered: asynchronous, with no bound on the relative speed of the agents, and synchronous, with synchronized clocks and equal speeds. The study focuses ring networks and investigates the conditions for complete edge exploration based on the initial energy levels of the agents.