This cryptic will be more interesting if you have a knowledge of German. VIER and NEUN are both perfect squares. If you were told the number represented by VIER, you could deduce the number represented by NEUN.

Alternatively, if you were told the number represented by NEUN, you could deduce the number represented by VIER.

What are the values of VIER and NEUN? (The same letter has the same value in both words, and there are no leading zeros.)