Alright: if x is the units digit and y is the tens digit, then your number will be:
10y + x .
for example , 24 = 10(2) + 4 .
When it's changed round it will be: 10x + y
for the above example, 42 = 10(4) + 2

So, your number is 10y + x ;when it is reversed 10x + y and it increases by 18.

i.e. number with digits reversed = original number + 18 .

i.e. 10x + y = (10y + x) + 18,hence 9x - 9y = 18

i.e. x - y = 2 -----------(1)

More over units digit = double that of tens digit ,

i.e. x = 2y ---------(2)

Now you have to solve the system of two equations with two unknowns:

x - y = 2 and x = 2y .

Good Luck
Ps:The answer is already present within the post!