With progress in technology and unceasing improvement in the standard of living, the practical scope of cloud computing is increasing day by day. Over the years, power consumption has become an important cost factor for computing resources. Because of this, management of energy has become critical for the implementation of networks and the pivotal target of all algorithms. A new metaheuristic task scheduling algorithm Discrete Symbiotic Organism Search (DSOS) algorithm was proposed recently, which focused on optimizing makespan but not from energy efficiency point of view. In this paper, a new energy aware optimization approach towards DSOS known as Energy aware Discrete Symbiotic Organism Search (E-DSOS) has been proposed for small-scale cloud networks. The detailed description and performance test results of both the original algorithm and its energy-efficient version are included. The experimental results prove that E-DSOS consumes lesser energy as the problem size increases.