\[\boxed{\text{638\ (638).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x^{2} - 10x + q = 0;\ \ \text{\ \ }x_{1} - x_{2} = 6\]
\[по\ теореме\ Виета:\]
\[x_{1} + x_{2} = 10;\ \ \ x_{1}x_{2} = q,\ тогда:\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = 10 \\ x_{1} - x_{2} = 6 \\ \end{matrix} + \right.\ \]
\[x_{1} + x_{2} + x_{1} - x_{2} = 10 + 6\]
\[2x_{1} = 16\]
\[x_{1} = 8\]
\[x_{1} + x_{2} = 10\]
\[x_{2} = 10 - 8 = 2\]
\[q = x_{1}x_{2} = 8 \cdot 2 = 16\]
\[Ответ:q = 16.\ \ \]