Increasing the deployment of Renewable Energy Resources (RES), along with innovations in Information and Communication Technologies (ICT), would allow prosumers to engage in the energy market and trade their excess energy with each other and with the main grid. To ensure an efficient and safe operation of energy trading, the Peer-to-Peer (P2P) energy trading approach has emerged as a viable paradigm to provide the necessary flexibility and coordinate the energy sharing between a pair of prosumers. The P2P approach is based on the concept of decentralized energy trading between prosumers (i.e., production capabilities or energy consumers). However, security protection and real-time transaction issues in the P2P market present serious challenges. In this paper, we propose a decentralized P2P energy trading approach for the energy market with high penetration of RE. First, the P2P energy market platform proposed coordinating the energy trading between energy providers and consumers to maximize their social welfare. A distributed algorithm is applied to solve the market-clearing problem based on the Alternating Direction Method of Multipliers (ADMM). In this way, the computational complexity can be reduced. Furthermore, a P2P Manager (P2PM) utility is introduced as an entity to solve the synchronization problem between peers during the market clearing. Finally, through a real-time application using Hardware-In-the-Loop (HIL), the effectiveness of the proposed P2PM is verified in terms of synchronizing the market participants and improving the power transaction.