In current LTE deployments, the unsupervised and unilateral installation of home or localized base stations, so called eNodeBs, may easily lead to excessive energy consumption and over-provisioning of network infrastructure. In this paper, we propose an energy efficient framework, which dynamically adjusts the power requirements of the system and performs Resource Block (RBs) allocation based on needs. It specifically optimizes power consumption of LTE networks consisting of under-utilized eNodeBs. The Energy Efficiency (EE) issue is formulated as an optimization problem, which trades off EE for SE without adversely impacting the downlink throughput. In order to solve this problem, we develop a heuristic approach called as Two Phase Enhanced Branch and Bound Algorithm (TPEBB) . End-to-end latency, modeled by Markov queues, is used as the main metric for QoS in this study . Finally, we compare the proposed framework with various competing methods to show almost 70% improvement in EE and end-to-end latency.