Accurate measurements of the edge plasma equilibrium profiles, including the temperature and density of electrons and ions, are critical to understanding the characteristics of the scrape-off layer (SOL) and divertor plasma transport in magnetically confined fusion research. On the J-TEXT tokamak, a multi-channel retarding field analyzer (RFA) probe has been developed to study edge plasma equilibrium profiles under various poloidal divertor and island divertor configurations. The edge radial profile of the ion-to-electron temperature ratio, τ_{i/e}, has been determined, which gradually decreases as the SOL ion self-collisionality, ν_{SOL}^*, increases. This is widely consistent with what has been observed previously from various tokamak experiments. However, the comparison of experimental results under different configurations shows that in the poloidal divertor configuration, even under the same ν_{SOL}^*, τ_{i/e} in the SOL region becomes smaller as the distance from the X-point to the target plate increases. In the island divertor configuration, τ_{i/e} near the O-point is higher than that near the X-point at the same ν_{SOL}^*, and both are higher than the limiter configuration. These results suggest that the magnetic configuration plays a critical role in the energy distributions between electrons and ions at the plasma boundary.