\[S_{10} = \frac{2a_{1} + 9d}{2} \cdot 10 =\]
\[= 5 \cdot \left( 2a_{1} + 9d \right)\]
\[a_{1} = 2 - \sqrt{2};\ \ d = \sqrt{2}:\]
\[S_{10} = 5 \cdot \left( 2 \cdot \left( 2 - \sqrt{2} \right) + 9\sqrt{2} \right) =\]
\[= 5 \cdot \left( 4 - 2\sqrt{2} + 9\sqrt{2} \right) =\]
\[= 5 \cdot \left( 4 + 7\sqrt{2} \right) =\]
\[= 20 + 35\sqrt{2}.\]