The rapidly increasing number of Internet of Things (IoT) devices is forecast to exceed 75 billion by 2025, driving demand for energy-efficient computing frameworks to support data-intensive applications in emerging technologies such as smart cities, healthcare, and industrial automation. Edge-cloud computing architecture leverages both edge processing capacity and centralized cloud processing capacity to address the inherent limitations of edge processing, namely energy costs associated with limited resources at the edge or transmission costs (including energy and delay) associated with sending data back and forth to the cloud. In this paper, an Energy-Aware Task Offloading (EATO) algorithm is proposed that dynamically offloads tasks to edge devices, edge servers, and the cloud for optimized energy consumption and quality of service (QoS). The EATO algorithm utilizes real-time energy profiling, network conditions, and computational requirements, and is calculated as a mathematical optimization problem. The EATO algorithm was evaluated using a simulation of 100 IoT devices and found to reduce energy consumption by up to 25% compared to edge-only and cloud-only approaches, while producing a 21% enhancement in task scheduling time over state-of-the-art methods [15]. The paper makes two main contributions: a generic, scalable task offloading framework and an examination of hybrid-based architecture for sustainable computing. The findings will encourage researchers to focus on energy efficiency for IoT deployments, and future work will investigate the coordination of these systems with real-world implementations and renewable energy sources.