Well, the TI-89 seems to think this is an impossible problem. No real solutions, no nonreal/i-term solutions.
The farthest I can get it by hand is:
sqrt(t - 42) - sqrt(t + 44) = 83
sqrt(t - 42) = 83 + sqrt(t + 44)
t - 42 = 166*sqrt(t + 44) + t + 6933
-6975/166 = sqrt(t + 44)
Unless I'm being terribad at math, this suggests that t=i*47438161/27556
In decimals, t=1721.518*i
However, when plugged into the original equation this is untrue (you get -1.036 = 83)
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