Energy efficiency (EE) is currently the key performance evaluation metric for wireless networks. This paper considers the maximization of EE of an uplink wireless network that uses single-carrier frequency division multiple access. The EE metric considered is bits/Joule, and a joint power and subchannel allocation problem is formulated to maximize this EE metric under constraints on the minimum achieved data rate of each user, the maximum transmit power budget of each user, and the exclusive as well as the consecutive allocation of single-carrier frequency division multiple access subchannels among the users. This problem is a nonlinear and combinatorial optimization problem, and its optimal solution is prohibitively difficult. To make the problem tractable and find its optimal solution, it is transformed into an equivalent binary integer programming problem, which is a standard set partitioning problem. This approach named as the optimal energy-efficient (OPT-EE) algorithm finds optimal solution with significantly reduced computational complexity compared to the solution of the original problem. In addition, a heuristic suboptimal energy-efficient approach is also investigated, which has acceptable performance with much less computational complexity compared to the OPT-EE algorithm. Simulation results demonstrate the performance of OPT-EE and heuristic suboptimal energy-efficient algorithms and their comparison with the available work in the literature.