No, E =/= I because you've already said "E = G, otherwise E = I".
In other words, if E = G is true, then E = G. If not, E = I. If they were the same, it would violate the law of non-contradiction, since what the statement is saying is I = ¬G (I is NOT G), and the law of non-contradiction in this context is ¬(G ^ I) (NOT G AND I).
You can have one or the other, not both.
In other words, if E = G is true, then E = G. If not, E = I. If they were the same, it would violate the law of non-contradiction, since what the statement is saying is I = ¬G (I is NOT G), and the law of non-contradiction in this context is ¬(G ^ I) (NOT G AND I).
You can have one or the other, not both.