I would disagree with the second equation, though I found that it gives a solution quite close to the one I got using another equation.

And that other equation is:

v^2 = u^2 - 2as

T_2 from your second equation is not an exact time.

It's only the red part that takes 4.15s, and the remaining black path for the stone that was thrown up takes the difference in time.

The time to go up is not necessarily the same it takes for the other black path near to the bottom of the cliff.