BFE stands for “bum fuck Egypt.” As I understand (and other
people have corroborated), it derives its existence from another expression “bumble fuck” (I am unsure if it's one word or two), both of which mean "out in the middle of nowhere." I am fairly certain that the inaccurate “butt fuck Egypt” derived from bum being the English term for buttocks. Clearly the
definition of BFE is the same regardless of what
one believes the “B” stands for, but I thought is was worth correcting.