# [J], 37 bytes

    +^:((=1#.,.&.":)*:[=]|~10^#@":@[)^:_~

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                                        ~    A = N
    +^:                              ^:_     while(...)A+=N; return A
       ((    ,.&.":)                )        digits of A
       (( 1#.      )                )        sum
       ((=         )                )        equals N
       (                ]|~10^#@":@[)        A mod (10^number of digits in N)
       (              [=            )        equals N
       (            *:              )        not AND
[J]: http://jsoftware.com/