OK, this was really fast, but software was used to get the symbolic solutions.
This is a pretty-printed result
Here is the c-code output.
‘T_l = -(wsqrt(pow(x_l-x_t,2.0)+pow(y_l-y_t,2.0))(x_r-x_t))/(x_ly_r-x_ry_l-x_ly_t+x_ty_l+x_ry_t-x_ty_r);’
‘T_r = (wsqrt(pow(x_r-x_t,2.0)+pow(y_r-y_t,2.0))(x_l-x_t))/(x_ly_r-x_ry_l-x_ly_t+x_ty_l+x_ry_t-x_ty_r);’
It was done really quick, so there may be errors. I apologize that I didn’t use your original variable names.