\[\sqrt{\left( \sqrt{39} - 7 \right)^{2}} - \sqrt{\left( \sqrt{39} - 6 \right)^{2}} =\]
\[= |\sqrt{39} - 7| - |\sqrt{39} - 6| =\]
\[= 7 - \sqrt{39} - \sqrt{39} + 6 =\]
\[= 13 - 2\sqrt{39}\]