[math-fun] 10 equations in 10 unknowns

Here are 10 equations in 10 unknowns: A + E + D - L = a E + Z + U - H = b N + D - V - Z = c S + U - V - A = d A + Z - V - E = e A^2 + E^2 + D^2 - L^2 = f E^2 + Z^2 + U^2 - H^2 = g N^2 + D^2 - V^2 - Z^2 = h S^2 + U^2 - V^2 - A^2 = i A^2 + Z^2 - V^2 - E^2 = j I am looking for algebraic solutions: A = f1(a, b, ..., j) D = f2(a, b, ..., j) ... Do you have a computer math package that can solve this problem (if solvable)? Christian.