x, y are the 2 digits.
x + y = 7
what is the value of the 2-digit numbers ?
well, the value of a number is given by the power of 10 of each position multiplied by the digit in that position.
e.g. the value of 456 is actually
456 = 4×10² + 5×10¹ + 6×10⁰
the value of the first number is therefore
x×10¹ + y×10⁰ = 10x + y
the cake if the second number (with reversed digits) is then
y×10¹ + x = 10y + x
and we know that the second number is smaller by 63 than the first number.
so,
10y + x + 63 = 10x + y
it if the first equation x + y = 7 we get e.g.
x = 7 - y
and use that in the main equation :
10y + (7 - y) + 63 = 10(7 - y) + y
10y + 7 - y + 63 = 70 - 10y + y
9y + 70 = 70 - 9y
18y = 0
y = 0
x = 7 - y = 7 - 0 = 7
so, the original number is 70.
the reversed number is 07 or simply 7.