Write a pair of irrational numbers whose difference is irrational.

Let $\sqrt{5} + 5 \text{ and } \sqrt{2} + 5$ be two irrational numbers.

Difference of numbers

$= \sqrt{5} + 5 - (\sqrt{2} + 5) \\[1em] = \sqrt{5} - \sqrt{2} + 5 - 5 \\[1em] = \sqrt{5} - \sqrt{2}.$

$\sqrt{5} - \sqrt{2}$ is an irrational number.

Hence, required pair = $\sqrt{5} + 5 \text{ and } \sqrt{2} + 5$.