Remembering that:

E + E = E

O + O = E

E + O = O

To discuss individual letters it's easiest to represent the sum as:

A B C

D E F +

--------

G H I J

The largest values for A and D are 6 and 8, which makes G = 1.

Since column 2 is E + O = O there can be no carry from column 1 (since E + O + 1 is always even). Therefore C and F are 3 and 5 (but we don't yet know which is which), therefore J = 8.

There can't be a carry from column 2 (as A + D is even) therefore E can't be 9 as this would force a carry.

Therefore I = 9. Hence B can't be 0. Therefore H = 0.

The last remaining odd number makes E = 7. Making B = 2.

Therefore A and D are 4 and 6 (but we don't yet know which is which).

Since the top row's digits have to add to 9 the top number must be 423.

This makes the sum 423 + 675 = 1098. QED.