Mobile edge computing (MEC) systems face unevenly distributed communication and computation traffics over both time and space. In order to match with the traffics, it is beneficial for different neighboring MEC systems to cooperate in sharing their distributed communication and computation resources. This paper considers two neighboring MEC systems each with one access point (AP) serving one user, where each user can offload the computation tasks to the respective AP for remote execution. We propose a new joint computation and spectrum cooperation approach, such that the two systems can share their computation and spectrum resources to enhance their respective system performance. In particular, we minimize the weighted sum energy consumption (for both communication and computation) of the two MEC systems, by jointly optimizing the task offloading decisions at the users (for computation resource sharing) and the spectrum bands shared between the two systems. We obtain the optimal solution to the formulated problem in a semi-closed form by applying standard convex optimization techniques. Numerical results show that the proposed joint cooperation design significantly reduces the energy consumption of the two systems, as compared to other benchmark schemes without such joint cooperation.