This manuscript proposes a hybrid method to effectively manage the energy on electric vehicle charging station (EVCS) and distribution system. The proposed method is consolidation of shell game optimization (SGO) and recalling-enhanced recurrent neural network (RERNN) named SGO-RERNN technique. The main aim of this work is to offer maximal amount of energy in this system and charging plans for EVCSs. The hybrid SGO-RERNN system is used to obtain the balancing solution. The intention of the distribution system is to maximize the planning charged for EVCSs. The proposed algorithm is related to supply function equilibrium method and it is used to modify and examine the interaction of each electric vehicle charging known as leader and the distributed system is known as follower. The hybrid SGO-RERNN technique is used to acquire the equilibrium solution. The SGO-RERNN system is implemented on MATLAB platform and the performance is compared to existing systems. Furthermore, the EVCS and distribution system efficiency is analyzed with the help of proposed method. The SGO-RERNN method attains electric vehicle charging station 1 attains 600.234, electric vehicle charging station 2 attains 3509.19, electric vehicle charging station 3 attains 4413.09, and distribution system attains 4327.033. The experimental outcomes prove that the integrated energy system costs minimized 3.89% and gains maximized to 7.8%. Finally, the SGO-RERNN method locates the optimum global solutions efficiently and accurately over the existing methods.