Unmanned aerial vehicles (UAVs) with integrated computing platforms can be used to provide computing offloading services for ground user equipments (UEs) with limited local computing capabilities, especially in remote areas. In this paper, we focus on the task offloading in an aerial edge network (AEN) assisted by a UAV. We aim at minimizing the sum energy consumption of all UEs by the joint optimization of the task offloading decisions and the UAV position under the constraints of the latency and the total energy of UAV. The formulated optimization problem is a mixed-integer nonconvex problem and involves coupling of many optimization variables. To address this challenge, we first transform the original optimization problem into a linear convex optimization problem via reformulation linearization technology, and then the alternating direction method of multipliers (ADMM) algorithm is proposed to achieve the approximate optimal solution. Numerical results confirm that the proposed ADMM algorithm can effectively reduce the total of energy consumption of UEs and ensure the continuous operation of the UEs.