At one period the Ancients recognised four elements:

                Fire
             Air    Earth
                Water

Solve the following base10 alphametric when the elements are in balance according to:
FIRE + EARTH = AIR + WATER,
and AIR wholly divides FIRE.

Note that by ignoring "AIR wholly divides FIRE" there are three other solutions to the alphametric.

Analytical solutions (PnP) can be reasonably achieved.