Considering two users exchange computational results through a two-way relay equipped with a mobile-edge computing server, we investigate the joint optimization problem of cooperative communication and computation, whose objective is the total energy consumption minimization subject to the delay constraint. To derive the low-complexity optimal solution, by assuming that the transmit power of the relay is given, we theoretically derive the optimal values of computation task partition factors. Thus, the optimal solution to the total energy consumption minimization problem can be found by one-dimensional search over the transmit power of the relay. Simulation results show that our proposed scheme performs better than that where all computational tasks are allocated to the relay or users.