\(x;\ y-the\ numbers\\\\ \left\{\begin{array}{ccc}xy=9\\x+y=10&\to x=10-y\end{array}\right\\\\subtitute\\\\(10-y)y=9\\10(y)-y(y)=9\\10y-y^2=9\\-y^2+10y-9=0\ \ \ |change\ signs\\y^2-10y+9=0\\y^2-y-9y+9=0\\y(y-1)-9(y-1)=0\\(y-1)(y-9)=0\iff y-1=0\ or\ y-9=0\)
\(\boxed{y=1\ or\ y=9}\\\\subtitute\ the\ value\ of\ y\ to\ x=10-y\\\\x=10-1\ or\ x=10-9\\\\\boxed{x=9\ or\ x=1}\\\\Answer:\boxed{\boxed{1\ and\ 9}}\)