Utility maximization is a major priority of prosumers participating in peer-to-peer energy trading and sharing (P2P-ETS). However, as more distributed energy resources integrate into the distribution network, the impact of the communication link becomes significant. We present a multi-commodity formulation that allows the dual-optimization of energy and communication resources in P2P-ETS. On one hand, the proposed algorithm minimizes the cost of energy generation and communication delay. On the other hand, it also maximizes the global utility of prosumers with fair resource allocation. We evaluate the algorithm in a variety of realistic conditions including a time-varying communication network with signal delay signal loss. The results show that the convergence is achieved in a fewer number of time steps than the previously proposed algorithms. It is further observed that the entities with a higher willingness to trade the energy acquire more satisfactions than others.