In this paper, we consider a downlink non-orthogonal multiple access (NOMA) enabled heterogeneous small cells network (HSCN), where the macro base station simultaneously communicates with multiple small cell base stations (SBSs) through wireless backhaul. In each small cell, users are grouped by NOMA bases and then served by their respective SBS. The proposed framework considers the realistic imperfect channel state information and quality of service requirements of users. The goal is to investigate an energy-efficient joint power, and bandwidth allocation scheme, which aims to maximize the energy efficiency (EE) of the small cells in downlink NOMA-HSCN constrained by the maximum transmit power and the minimum required data rate simultaneously. The optimization problem is non-convex due to the fractional objective function and non-convex constraint and thus challenging to obtain an exact solution efficiently. To this end, the joint optimization is first decomposed into two subproblems. Then, an iterative algorithm to solve the power optimization subproblem is proposed with guaranteed convergence. Furthermore, we derive a closed-form solution for the bandwidth allocation subproblem. Simulation results reveal that the effectiveness of the proposed schemes in terms of EE compared to the existing NOMA and the orthogonal multiple access schemes.