The energy efficiency in wireless networks is a central concern of research. We propose in this paper a new energy efficiency scheme which allocates the mobile's transmission power in function of the allocated Resource Blocks (RB) and the channel conditions of the user on the allocated RBs. We focus on the energy efficiency of the Opportunistic and Efficient Resource Block Allocation (OEA) algorithm and its variant adapted to the Quality of Service (QoS) of the traffics: the QoS based OEA for LTE uplink networks. The OEA and the QoS based OEA allocate the RBs to UEs efficiently and with respect to the SC-FDMA constraints, such that, for one user, contiguous RBs are allocated, and the same Modulation and Coding Scheme (MCS) is used over the whole allocated RBs. Once RBs are allocated to UEs, power control is then applied to the mobile's transmission power considering the MCS used and the channel conditions. This energy efficiency allows users to achieve the same throughput than before the power control and does not affect the MCS selection established at the RB allocation step. This new scheme allows the transmission of a high number of bits per Joule.