I don't understand Qxcos240... Do you mean Qcos240? ie: Qx = Qcos240?
I don't think this method is correct... It is impossible for both tensions to be 270N at the same time.
I recommend going with what I said earlier... use T1 and T2 as variables.... solve for them in terms of Q... then you can see what limits are required to make T1 and T2 remain less than 270.