The energy evolution in buoyancy-generated turbulence subjected to shear depends on the gradient Richardson number Ri and the stratification number St, which is a ratio of the time scale of the initial buoyancy fluctuations to the time scale of the mean stratification. During an initial period, the flow state evolves as in the unsheared case. After this period, shear generates fluctuating velocity components for St=0.25, but it depletes the fluctuating vertical velocity component and temperature variance faster than in the unsheared case for St=4. Weak shear causes the kinetic and total energy to decrease faster than in the unsheared case, whereas strong shear adds more energy in comparison with the unsheared case. Energy increased with time in only one case considered (St=0.1 and Ri=0.04). When St>1, the nonlinearity of the flow does not become significant even when Ri is small. Thus, results from rapid distortion theory and direct numerical simulation compare well. In particular, the theory reproduces trends in the energy evolution for St>1.