Start by squaring:

(t-169) + (t+36) - 2[(t-169)(t+36)]^{1/2} = 43^2

rearrange:

[(t-169)(t+36)]^{1/2} = 991 - t

square again:

(t-169)(t+36) = (t-991)^2

which reduces to:

1849 t - 988165=0

Now the games we have played may have introduced spurious solutions

so each solution has to be checked to see if it actualy solves the equation.

Doing this we find that t=988165/1849 is not a solution of the given

equation, so there are no solutions to the equation.

Reassuringly when fed to quickmath (which IIRC is Mathematica powered)

and Derive they both also report no solutions.

RonL

(check the algebra - it can be a bit error prone)