This sounds like the Foundation series by Isaac Asimov. Two planets at the ends of the universe were set up by Hari Seldon, a psychohistorian to optimise the recovery of the Galactic Empire from a state of anarchy. The Galactic Empire was also ruled by an Emperor from the planet Trantor, the capital.
One of the planets, Terminus, was meant to specialise in technology and collect scientific knowledge whilst the other reportedly consisted of mentalists and psychological experts with supernatural abilities. The inhabitants of Terminus are unaware of the location of the second planet and a major part of the plot involves locating and interacting with this other planet.