18. Solve the congruence equation $\left(x^{2}+1\right)(x+1) x \equiv -1(\bmod 41)$.
18. The original equation is $x^{4}+x^{3}+x^{2}+x+1 \equiv 0(\bmod 41), x \equiv 1(\bmod 41)$ is not a solution, so the solutions to the original equation are the solutions to $x^{5} \equiv 1(\bmod 41)$ excluding $x \equiv 1(\bmod 41)$, which are
$$x \equiv 10,18,16,37(\bmod 41)$$