Mental Energy is a very hard-to-master source of power. When used, it is mentioned to be a less draining way to use telekinesis, and it is essential for doing a brain push. It takes many years to store such energy, and many more to practice this mental power. With Sophie being the only known exception, it is thought that only Ancients can perform using such energy.
Shown through the Ultimate Splotching Championship, mental energy does not mix with core energy, causing an extreme rebound. It is likely that Sophie only knows how to do this trick because Mr. Forkle would train her mind at night pre-Keeper.