You want to solve for x_1, which will tell you how much things were translated horizontally; after that it's easy to figure out how much things were translated vertically. One way to solve for x_1 is to rewrite v and s in terms of exponentials. Let P = e^(x_1 / a), Q = e^(x_2 / a). Then...
v = a(e^(x_2 / a) + e^(-x_2 / a))/2 - a(e^(x_1 / a) + e^(-x_1 / a))/2
= a (Q + 1/Q - P - 1/P)/2
s = a(e^(x_2 / a) - e^(-x_2 / a))/2 - a(e^(x_1 / a) - e^(-x_1 / a))/2
= a (Q - 1/Q - P + 1/P)/2
=> (s+v)/a = Q - P
=> (s-v)/a = 1/P - 1/Q = (Q-P)/(QP) = (s+v)/a * 1/(QP)
=> QP = (s+v)/(s-v)
=> e^((x_2 + x_1) / a) = (s+v)/(s-v)
=> (x_2 + x_1) / a = ln( (s+v) / (s-v) )
=> x_2 + x_1 = a ln( (s+v) / (s-v) ) == A
Since x_2 - x_1 = h, we now have
x_1 = (A - h) / 2
= (a ln( (s+v) / (s-v) ) - h) / 2
You should double-check my derivation. There are probably simpler methods.
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