Eniac was the first electronic computer, more or less. It was intended to work out trajectory tables for bombs and mortars during WWII, but as with some many computer-oriented projects, the schedule slipped. They ended up using it to do some solid work on the h-bomb though.
A difference engine is a historical, mechanical special-purpose computer designed to tabulate polynomial functions. Since logarithmic and trigonometric functions can be approximated by polynomials, such a machine is more general than it appears at first.
Charles Babbage designed the difference engine in 1834. He never even finished building one. In 1985 the British Science Museum started building one and completed it in 1991. It's said by many that he intended to use it make a killing at the horse-races.
Some guy built a freaking difference engine out of LEGO.