Let the larger number \(=x\)
Then the square of the smaller number \(=8\) times the larger number \(=6 x\)
and the square of the larger number \(=x^{2}\)
According to the question,
$$
\begin{aligned}
&x^{2}-6 x=100 \\
&=x^{2}-8 x-100=0 \\
&=x^{2}-10 x-10 x-100=0 \\
&=x(x-10)+10(x-10)=0 \\
&\Rightarrow(x-10)(x+10)=0 \\
&\Rightarrow x-10=0 \text { or } x-10=0 \\
&\Rightarrow x=10 \text { or } x=-10
\end{aligned}
$$
Thus, the larger number \(=18\) or \(-10\)
Then, the square of the smaller number \(=0(10)\) or \(0(-10)\)
$$
=144 \text { or }-00
$$
The square of a number can't be negatlve, so, the square of smaller number = 144
Hence, the smaller number \(=\operatorname{sqrt}(144)=12\)
The numbers are 12 and 18
