Mobile edge computing (MEC) has recently become a promising paradigm to meet the increasing computing requirement of mobile devices, and hybrid energy supply has been considered as an effective approach for saving the energy consumption of the MEC system and making it environmentally friendly. In particular, the joint task scheduling and energy management (TSEM) scheme plays a crucial role in reaping the benefits of MEC with hybrid energy supply. In this article, we focus on jointly optimizing the TSEM decisions to maximize the utility of the MEC system which accounts for both the computation throughput and the fairness among different cells, by formulating a stochastic optimization problem subject to the constraints of queue stability and energy budget. We transform the formulated problem into a deterministic problem and then decouple it into four independent subproblems, which can be solved in a distributed manner without future system statistical information. An online TSEM algorithm is developed to derive the optimal solutions to these subproblems. Mathematical analysis shows that TSEM can achieve a close-to-optimal system utility and realize the utility-queue tradeoff. The experimental results validate the advantages of TSEM in improving the system utility and stabilizing the queue length.