performance tuning – How to speed up integers finding function?


Playing with integers I looked for a way of finding, let’s say, $4$-digits positive integers such that $a,b,a+b$ had the same digits, like $$1089 + 8019 = 9108$$
I am a newbie and I used this function

sd[a_, b_] := 
 If[Mod[a, 9] != 0 || Mod[b, 9] != 0 , False, 
  Sort[IntegerDigits[a + b]] == Sort[IntegerDigits[a]] && 
   Sort[IntegerDigits[a]] == Sort[IntegerDigits[b]]]

Then I used the function in this way

Select[Flatten[
  Table[{h, k, sd[h, k]}, {h, 1000, 10000}, {k, h, 10000}], 1], #[[3]] &]

But it took ages to give the output.

Is there a way to speed up this procedure?

Thanks in advance