If an integer $n > 8$ is a solution of the equation $x^2 - ax+b=0$ and the representation of $a$ in the base-$n$ number system is $18$, 
then the base-n representation of $b$ is
$\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 80 \qquad \textbf{(D)}\ 81 \qquad \textbf{(E)}\ 280$
Assuming the solutions to the equation are n and m, by Vieta's formulas, $n_n + m_n = 18_n$.  
$n_n = 10_n$, so $10_n + m_n = 18_n$.  
\[m_n = 8_n\].
Also by Vieta's formulas, $n_n \cdot m_n = b_n$. 
\[10_n \cdot 8_n = \boxed{80_n}\].
The answer is (C) $80$