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In unmanned aerial vehicle (UAV)-enabled wireless networks, UAVs carry the base station (BS) to flexibly provide wireless communication services, supporting data transmission in high-quality wireless channel conditions. Meanwhile, deploying the mobile edge computing server on the UAV brings the computing resource closer to users. By offloading tasks to the mobile edge computing server, the tasks can be processed directly on the BS, alleviating the pressure on the fronthaul link. However, with the consideration of the constrained energy consumption, how to reduce the energy consumption while ensuring the stability of data transmission and task processing from users to the BS remains a challenging problem. Considering that users send data and offload computing tasks to the BS in the UAV-enabled wireless networks, the energy consumption minimization problem is researched with allocating the radio and the computing resources, constrained by the stability of the data transmission queues and the task processing queues. The data queues and the task queues are involved, in which the Lyapunov optimization theory is utilized to transform and decompose the optimization problem into the convex programming. A trade-off between the energy consumption and the queue length is obtained. The effectiveness of the proposed solution is evaluated through the simulation analyses.