Despite numerous advantages, non-orthogonal multiple access (NOMA) technique can bring additional interference for the neighboring ultra-dense networks if the power consumption of the system is not properly optimized. While targeting on the green communication concept, in this paper, we propose an energy-efficient downlink resource allocation scheme for a NOMA-equipped cellular network. The objective of this work is to allocate subchannels and power of the base station among the users so that the overall energy efficiency is maximized. Since this problem is NP-hard, we attempt to find an elegant solution with reasonable complexity that provides good performance for some realistic applications. To this end, we decompose the problem into a subchannel allocation subproblem followed by a power loading subproblem that allocates power to each user's data stream on each of its allocated subchannels. We first employ a many-to-many matching model under the assumption of uniform power loading in order to obtain the solution of the first subproblem with reasonable performance. Once the the subchannel-user mapping information is known from the first solution, we propose a geometric programming (GP)-based power loading scheme upon approximating the energy efficiency of the system by a ratio of two posynomials. The techniques adopted for these subproblems better exploit the available multi-user diversity compared to the techniques used in an earlier work. Having observed the computational overhead of the GP-based power loading scheme, we also propose a suboptimal computationally-efficient algorithm for the power loading subproblem with a polynomial time complexity that provides reasonably good performance. Extensive simulation has been conducted to verify that our proposed solution schemes always outperform the existing work while consuming much less power at the base station.