[Algebra]
Problem: Let $T=362$ and let $K=\sqrt{T-1}$. Compute $\left|(K-20)(K+1)+19 K-K^{2}\right|$.

Solution: The expression inside the absolute value bars simplifies to $K^{2}-19 K-20+19 K-K^{2}=-20$. Hence the answer is $\mathbf{2 0}$ and the value of $K(=\sqrt{361}=19)$ is not needed.

Final answer: 20