Refractory high-entropy alloys (RHEAs) are considered as potential candidates for high-temperature applications, with the glide resistance of edge dislocations being a crucial factor in determining the high-temperature strength. However, the solid-solution strengthening mechanism of edge dislocations in RHEAs is not fully understood. The existing Labusch-type models mainly focus on the long-range interaction of solute atoms with the dislocation stress field, while there is little attention paid to the short-range interaction in the dislocation core region. Here, we conduct carefully designed atomic simulations to decouple the long-range and short-range interactions in a typical RHEA, NbMoTaW. Furthermore, the total change in solute-dislocation interaction energy is decomposed, and a hierarchical energy landscape is revealed, demonstrating that the short-range interaction at the core region gains more importance in the solid-solution strengthening of edge dislocations in NbMoTaW. Then, we determine the Larkin length, which signifies the transition from size-dependent to size-independent dislocation behavior. The activation barrier extracted from the simulation with the dislocation length above the Larkin length is incorporated into the crystal plasticity model, and the high-temperature yield strength is well predicted by the strengthening from edge dislocations. Our work provides deep insight into the solid-solution strengthening mechanism in random solution solids, elucidating the importance of the local atomic configuration around the dislocation core.