\[\sqrt{18 - 4\sqrt{14}} - \sqrt{63 - 14\sqrt{14}} =\]
\[= \left| \sqrt{14} - 2 \right| - \left| 7 - \sqrt{14} \right| =\]
\[= \sqrt{14} - 2 - 7 + \sqrt{14} =\]
\[= 2\sqrt{14} - 9\]