The difference between the squares of two consecutive numbers is 31.

Let the numbers be $x$ and $x+1$.

According to the question,

$(\mathrm{x}+1)^{2}-\mathrm{x}^{2}=31$

or $\mathrm{x}^{2}+2 \mathrm{x}+1-\mathrm{x}^{2}=31$

or $2 \mathrm{x}=31-1$

or $\mathrm{x}=\frac{30}{2}$

or $\mathrm{x}=15$

Thus, the numbers are 15 and 16 .