#Python 3, 130 bytes
Thanks to @Rod for pointing out a bug
from random import*
def f(x):l=10**len(x);k=str(randint(0,l-1)+l)[1:];print(''.join(chr(ord(i)+int(j))for i,j in zip(x,k))+'\n'+k)
A function that takes input via argument as a string and prints to STDOUT.
[Explanation and test link coming later]