While understanding breaking waves is crucial for the development of parametrizations used in ocean wave modeling for both deep and shallow water, the complete process of wave breaking is not well understood. Here we present direct numerical simulations of two-dimensional solitary waves that shoal and break on a uniform beach in shallow water, with the presence of storm surge represented by an inshore region. The storm surge depth, beach slope, and wave amplitude are varied to study the dependence of energy dissipation in the breaker on wave and bathymetric parameters. We classify wave breaker types and find a separation between plunging and spilling breakers when scaled by breaking amplitude and depth. We compare energy dissipation during the breaking process with results from the literature without storm surge. A representation of energy dissipation in this solitary wave breaker data is also compared with prior experiments and simulations of breakers in deep water, and possibilities of a unifying model are explored. We conclude that a previously developed shallow-water inertial dissipation model for wave breaking on a uniform slope can be extended to this storm surge environment with good data collapse, and we further discuss possibilities for a general parametrization of wave breaking valid across different depth regimes.