The professional tool that allows you to align your hole and drill from both sides of a solid material like brick accurately is called a Transpointer (e.x. Hilti PX10). Unfortunately they're usually around $1000, so that's probably not an option.
Drill your 10mm hole to a depth within 25mm of the face of the brick so that you don't blow out the other side, put a stack of neodymium button magnets (less than 10mm in diameter) into the hole, and then use one of the neodymium magnets on the other side of the hole to find the center blindly. If your hole depth is close enough to the surface, the magnet will either repel or be attracted to the center of the stack of magnets in the wall depending on which pole (North or South) you put nearest the wall.
Now you know exactly where the hole is and can drill the last 25mm from the blind side and prevent a blowout.