The number is 35
let the digit at one's place be y and that in 10's place be x
so the number is 10x+y
given 10x+y=3+4(x+y) ----- 1
and also given 10x+y+18=10y+x ------2
substituting 1 in 2 
gives 3+4(x+y)+18=10y+x
solving the above equation for x, you should get x=2y-7  ------3
now substitute 3 in 1
solving the above equation for y, you will get 9y=45 which gives y=5 ------4
substitute 4 in 3 and you get x=3
now the number is 10x+y= 10(3) + 5=35
there you go ^_^