Problem: VIER and NEUN are 4-digit squares

 > VIER and NEUN represent 4-digit squares, each letter denoting a
 > distinct digit. You are asked to find the value of each, given the
 > further requirement that each uniquely determines the other.
 >
 > The "further requirement" means that of the numerous pairs of
 > answers, choose the one in which each number only appears once
 > in all of the pairs.
                         -------- Is this easy to understand?
                                  (What the problem is asking?)
%   Problem: VIER and NEUN are 4-digit squares; determine distinct V, I,
%   E, R, N, and U, such that there is a unique solution (VIER,NEUN) for
%   some particular E.
                          --------  OK... that makes more sense.
it's kinda cute that (for solving by a Human)
                       the names  (VIER,NEUN)  can act as Hints.
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i wrote Python code that gives me a partial solution.
a Dictionary's  default  printed output is    Not too Great
{'1': 'n', '5': 'e', '2': 'u'}  {'4': 'v', '3': 'i', '5': 'e', '6': 'r'}
{'1': 'n', '5': 'e', '2': 'u'}  {'7': 'v', '0': 'i', '5': 'e', '6': 'r'}
I'd prefer:
               (1=n, 5=e, 2=u)  (4=v, 3=i, 5=e, 6=r)
               (1=n, 5=e, 2=u)  (7=v, 0=i, 5=e, 6=r)