Quantum dot (QD) solids are promising optoelectronic materials; further advancing their device functionality requires understanding their energy transport mechanisms. The commonly invoked near-field Förster resonance energy transfer (FRET) theory often underestimates the exciton hopping rate in QD solids, yet no consensus exists on the underlying cause. In response, we use time-resolved ultrafast stimulated emission depletion (STED) microscopy, an ultrafast transformation of STED to spatiotemporally resolve exciton diffusion in tellurium-doped cadmium selenide-core/cadmium sulfide-shell QD superlattices. We measure the concomitant time-resolved exciton energy decay due to excitons sampling a heterogeneous energetic landscape within the superlattice. The heterogeneity is quantified by single-particle emission spectroscopy. This powerful multimodal set of observables provides sufficient constraints on a kinetic Monte Carlo simulation of exciton transport to elucidate a composite transport mechanism that includes both near-field FRET and previously neglected far-field emission/reabsorption contributions. Uncovering this mechanism offers a much-needed unified framework in which to characterize transport in QD solids and additional principles for device design.