The digits of 3 digit natural number are in A.P = Arithmetic Progression that is we can write them as

x, x + k, x + 2k

Since they are digits they are elements of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Arithmetic progression (AP) is a sequence of numbers such that the difference between the consecutive terms is constant - in our case the difference is 'k'.

Their sum is 18:

x + x + k + x + 2*k = 18

3*x + 3*k = 18

x + k = 6

The number that we are looking for A = x + 10*(x+k) + (10^2)(x+2k)

Let B the number with reversed digits that is B = (x+2k) + 10*(x+k) + (10^2)*x

A - B = 594 that is

[x + 10*(x+k) + (10^2)(x+2k)] - [(x+2k) + 10*(x+k) + (10^2)*x] = 594

Lets find x and k as a solutions of the systems equations

x + k = 6

x + 10*(x+k) + (10^2)(x+2*k) - (x+2*k) - 10*(x+k) - (10^2)*x = 594

x = 3

k = 3

The digits are 3, 6, 9 hence the number is

A = x + 10*(x+k) + (10^2)(x+2k) = 963

Indeed 963 - 369 = 594.