#PHP, 73+1 bytes

while(array_sum(str_split($i+=$n=$argn))-$n|$i%10**strlen($n)-$n);echo$i;

Run as pipe with -R.

loops $i through multiples of <input> until sum_of_digits-<input> and tail_of_i-$n are falsy; then prints i.

PHP, 73+1 bytes

while(array_sum(str_split($i+=$n=$argn))-$n|$i%10**strlen($n)-$n);echo$i;

Run as pipe with -R.

loops $i through multiples of <input> until sum_of_digits-<input> and tail_of_i-$n are falsy; then prints i.

#PHP, 63+1 bytes

while(($i+=$n=$argn)%10-$n|array_sum(str_split($i))-$n);echo$i;

Run as pipe with -R.

loops $i through multiples of <input> until $i%10-<input> and sum_of_digits-<input> are falsy; then prints i.

#PHP, 73+1 bytes

while(array_sum(str_split($i+=$n=$argn))-$n|$i%10**strlen($n)-$n);echo$i;

Run as pipe with -R.

loops $i through multiples of <input> until sum_of_digits-<input> and tail_of_i-$n are falsy; then prints i.