[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ x&,& y~)
% (c,d)
&T&(~ 10 &,& 18~)
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{10+x}{2}~,~\cfrac{18+y}{2} \right)~~=~~\stackrel{midpoint}{(5,-8)}\implies
\begin{cases}
\cfrac{10+x}{2}=5\\\\
10+x=10\\
\boxed{x=0}\\
-------\\
\cfrac{18+y}{2}=-8\\\\
18+y=-16\\ \boxed{y=-34} \end{cases}[/tex]
