smc

Notice that $3\sqrt{11}-10=\sqrt{99}-\sqrt{100}<0$, $18-5\sqrt{13}=\sqrt{324}-\sqrt{325}<0$, and similarly, $10\sqrt{26}-51=\sqrt{2600}-\sqrt{2601}<0$, so these numbers can be excluded immediately as they are negative and we seek the smallest positive number. The remaining choices are $10-3\sqrt{11}=\sqrt{100}-\sqrt{99}$ and $51-10\sqrt{26}=\sqrt{2601}-\sqrt{2600}$. Observe that $\sqrt{100}-\sqrt{99}=\frac{1}{\sqrt{100}+\sqrt{99}}\approx \frac{1}{10+10}=\frac{1}{20}$, and $\sqrt{2601}-\sqrt{2600}=\frac{1}{\sqrt{2601}+\sqrt{2600}}\approx \frac{1}{51+51}=\frac{1}{102}<\frac{1}{20}$, so the smallest positive number in the list is $\boxed{51-10\sqrt{26}}$.