Answer by Sudhanshu Bharadwaj for Why energy is released (most of the time) when electrons are added to atoms?

This Because of the Decrease Potential Energy (of the attractive force) between the Nucleus and the electron (Which Dominates over the the increase in potential due to electron -electron interaction)

You can think of it as the electron "Falling down" the "Potential well" and thus releasing energy (like a ball which falls down hits the ground releasing energy)