We have a gas water heater and would like to change to a electric water heater. We have a 240 plug for dryer and a 110 plug for the washer. So how would we do the wiring.

I would try to pull more wires to dryer box, if in conduit, and go from there.
Depending on water heater. May need 2- #10's or 2- #12's. Could be 240 volts or 120 volts.
If 120 volts, You may be able to pull 1 hot wire from panel, and have on opposite phase
Of washer,
Removal of panel cover to determine conduit size easier than opening dryer recpticle.
Would keep washer and water heater separate.