Non-Orthogonal Multiple Access (NOMA) is a promising energy-efficient technology designed to satisfy the demands of future networks by efficiently sharing radio resources. In NOMA, the same radio resource is simultaneously assigned to two users at different power levels based on the NOMA-power domain. Resource allocation in NOMA presents a non-convex challenge, characterized as a non-deterministic polynomial (NP-hard) problem. This involves user and channel assignment and power allocation, making it an extraordinarily complex task to achieve an optimal solution. In this work, Simulated Annealing (SA) is proposed as an optimization technique for resource allocation in an energy-efficient downlink NOMA system. This resource allocation scheme addresses user and channel assignment, as well as power allocation, using SA as an efficient standalone approach to maximize energy efficiency in NOMA. SA is utilized to execute the assignment of users to channels, distribute the necessary power for each channel, and determine the power ratio among users sharing the same channel. The results obtained demonstrate a significant improvement in energy efficiency, outperforming the existing numerical methods by 22 %. The proposed SA scheme not only achieves a close optimal solution but also in less computational time, offering sufficient reliability in terms of energy efficiency enhancement when compared to the existing numerical method.