Two numbers differ by 26, and the greater of them is exactly three times the smaller. Find the greater number.

Let the numbers be $x$ and $y$ with $x$ the larger. $x-y=26$ and $x=3y$. Substituting: $3y-y=26$, so $2y=26,y=13$ and $x=39$. Check: 39 - 13 = 26 and $39=3\times 13$. 13 is the smaller number; 26 is the given difference itself; 52 is the sum of the two numbers, which is what you find if you read 'difference' as 'sum'.