Find the smallest positive number from the numbers below.
$\textbf{(A)} \ 10-3\sqrt{11} \qquad  \textbf{(B)} \ 3\sqrt{11}-10 \qquad  \textbf{(C)}\ 18-5\sqrt{13}\qquad \textbf{(D)}\ 51-10\sqrt{26}\qquad \textbf{(E)}\ 10\sqrt{26}-51$
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 $\boxed{\textbf{(D)} \ 51 - 10 \sqrt{26}}$.