We investigate a mobile edge computing (MEC) system that supports collaborative task offloading, allowing busy users to offload their tasks to the server and idle users, or perform them locally. However, executing computing tasks consumes device energy, making idle users unwilling to perform other users' tasks due to limited battery capacity. Additionally, the components of the total energy expenditure of the MEC system supporting collaborative task offloading are complex, necessitating appropriate resource allocation and offloading strategies to minimize the system's total energy consumption. To address these challenges, we propose a computing resource sharing auction (CRSA) algorithm to motivate idle users to participate in task offloading. Then, we establish a non-convex mixed-integer nonlinear programming (MINLP) problem to minimize the total energy consumed by the system. By utilizing the McCormick and continuous relaxation (CR) approaches, we develop a low-complexity resource allocation algorithm. Finally, the numerical results demonstrate the effectiveness of the proposed mechanism and resource allocation algorithm.