Equality in the sum of digits Introduction
Let's take the number 180. This is an interesting number because the sum of digits of this number is equal to:
1 + 8 + 0 = 9

And the squared version of this number, or:
180² = 32400 &gt; 3 + 2 + 4 + 0 + 0 = 9

These are both 9. The sum of digits of the original number and the squared number are the same. Of course, this is also found at OEIS: A058369.
Task
Given a non-negative integer n, output the nth positive number with this condition.
Test cases (zero-indexed)
Input &gt; Output

0 &gt; 1
1 &gt; 9
2 &gt; 10
3 &gt; 18
4 &gt; 19
5 &gt; 45
6 &gt; 46
7 &gt; 55
8 &gt; 90
9 &gt; 99
10 &gt; 100
11 &gt; 145
12 &gt; 180
13 &gt; 189
14 &gt; 190
15 &gt; 198
16 &gt; 199
17 &gt; 289
18 &gt; 351
19 &gt; 361

The input can also be 1-indexed if that fits you better.
This is code-golf, so the submission with the least amount of bytes wins!
Jelly, 13 bytes

,²DS€=/
1Ç³#Ṫ


Input is 1-indexed. Try it online!

How it works

1Ç³#Ṫ    Main link. Argument: n (index)

1        Set the return value to 1.
   #     Execute ... until ... matches have been found.
 Ç         the helper link
  ³        n
    Ṫ    Extract the last match.


,²DS€=/  Helper link. Argument: k (integer)

,²       Pair k with k².
  D      Convert each to decimal.
   S€    Compute the sum of each list of base 10 digits.
     =/  Reduce by equality.