The proliferation of cloud computing infrastructure has increased the energy demand remarkably. Energy-efficient resource management is essential for running a cost effective and environment friendly data center. Virtual Machine (VM) consolidation is a well-accepted method for reducing the energy consumption of the cloud data center. Quality of service is an equally important aspect of cloud services. VM migrations caused by consolidation often cause degradation in QoS. These two parameters have been dealt with individually in most research and very few addressed both energy efficiency and QoS simultaneously. We have proposed a new Energy and QoS Efficient (EQSE) VM selection and placement method for improving the energy efficiency along with quality of service (QoS). VM selection and placement are two critical steps of VM consolidation. EQSE uses Resource Gap Minimization (RGM) algorithm for VM selection and Utilization-Aware Best-Fit Decreasing (UABFD) algorithm for placement of these VMs. EQSE along with dynamic thresholds reduces energy consumption and improves the quality of service by reducing the number of VM migrations. CloudSim simulation performed on PlanetLab data establishes the superiority of the proposed method compared to the existing state of the art methods of VM consolidation.