Explanation

Let the number be abc.

abc + 99 = cba

100a + 10b + c +99 = 100c + 10b + a

99(c - a) = 99

c - a = 1

Also, a + c = b

& a + b + c = 10

so, 2b = 10

b = 5

Now, a + c = 5

c - a = 1

so, 2c = 6

c = 3 & a = 2

so, the required number is 253