The sum of the digits of a 2-digit number is 6.

Solution:

Let the two numbers of the two-digit number be 'a' and 'b'.

$a+b=6$      ....(1)

The number can be written as $(10 a+b)$.

After interchanging the digits, the number becomes $(10 b+a)$.

$(10 a+b)+18=(10 b+a)$

$9 a-9 b=-18$

$a-b=-2$               ..(2)

Adding equations (1) and (2):

$2 a=4 \Rightarrow a=2$

Using $a=2$ in equation (1):

$b=6-a=6-2=4$

Therefore, the original number is 24 .