White holes are VERY hypothetical. They are, in fact, predicted as a possible "other end" of a black hole that has punctured a "worm hole" through space, but black holes are most likely just a point in space without an other side. The matter/energy coming out of white holes is supposedly the matter falling into a black hole. They have only been seen discussed in theoretical physics talks. At one point scientists speculated that quasars may be white holes, but now we are fairly certain that quasars are powered by supermassive black holes, in which case the light we see comes from matter as it falls into the black hole. After it falls in, we assume the matter just becomes part of the black hole and does not come out anywhere.

Source: NASA