Vehicular Edge Computing (VEC) integrates edge computing with the Internet of Vehicles (IoV) to provide low-latency, high-reliability data processing near vehicles. While existing VEC resource allocation research often maximizes social welfare or minimizes delay, the critical aspect of energy consumption, which significantly impacts user Quality of Experience (QoE), is frequently overlooked. This paper addresses the joint resource allocation and task offloading problem in VEC, aiming to simultaneously optimize social welfare and minimize energy consumption. We formulate this as a mechanism design problem and decompose it into two sub-problems: Winner Determination (selecting which Vehicle Devices (VDs) offload tasks) and Offloading Decision (assigning tasks to specific Mobile Edge Computing (MEC) servers). For winner determination, we propose a truthful greedy algorithm that ranks VDs based on a weighted combination of their bid (representing social welfare contribution) and potential energy savings. For the offloading decision, we employ an approximation algorithm based on local search to minimize energy usage among selected VDs. The proposed overall mechanism is truthful, guaranteeing that VDs are incentivized to report their true valuations. Simulation results demonstrate that, compared to recent algorithms, our approach improves energy savings by 8%-12% in high-competition scenarios with only a minor (1%-2.5%) reduction in social welfare. In low-competition environments, our mechanism enhances energy savings by approximately 6% while concurrently increasing social welfare by about 2%.