The advancement of Internet of Everything (IoE) propels the fast growth of next-generation, such as 6G networks, leading to a new era of coverage, connectivity, and technological innovation, which calls for novel approaches to address rising energy consumption and maximize resource use. The proposed article presents a robust hybrid algorithm that combines leader-based optimization and Adaptive Differential Evolution (DE) in the framework of the Energy Efficient Hybrid Evolutionary Algorithm (EEHEA), which is specifically designed for the complex environment of IoE-enabled 6G networks. The scheme EEHEA combines the efficacy of leader-based optimization (LBO) for an effective decision-making process and adaptive differential evolutionary optimization (ADE) 's dynamic network-parameters adaptation, enhanced convergence, and global searching ability, persistently fine-tuning optimization strategies based on the dynamics of the network. Combining these components into the scheme EEHEA allows it to balance local exploitation and global exploration effectively. This implies better resource allocation and improved energy efficiency in ecosystems with IoE-driven 6G (IoE-6G). The outcomes report that the scheme EEHEA can address the rising energy consumption issues and enhance the efficiency of IoE-6G. Based on simulation experiments, the proposed scheme EEHEA can demonstrate faster convergence times, higher accuracy, and superior flexibility concerning changing network conditions. Its capability to handle energy-related challenges and navigate complex network environments with resilience shows the ability to enhance the performance of IoE-6G. The EEHEA scheme reports its efficacy over state-of-the-art schemes regarding localization, latency, coverage, and energy expenditure performance metrics.