05AB1E, 8 (or 10?) 11 (or 13?) bytes
Ÿʒ₄n+¦S3ôOË
Try it online or verify some more test cases.
NOTE: In 05AB1E strings and integers are interchangeable, so the output numbers doesn't contain leading zeroes. This could however be fixed with 1 additional byte (12 bytes):
Ÿ₄n+€¦ʒS3ôOË
Try it online or verify some more test cases.
+3 bytes to bug-fix numbers with a length of 3 or less (range [000000, 000999]).
Explanation:
Ÿ # Create an inclusive (on both sides) range from the two inputs
# i.e. 038920 and 038910 →
# [38910,38911,38912,38913,38914,38915,38916,38917,38918,38919,38920]
ʒ # Filter this list by:
₄n+ # Add 1,000,000 to the number
| # And remove the leading 1
# i.e. 38910 → 1038910 → '038910'
S # Transform it to a list of digits
# i.e. '038910' → ['0','3','8','9','1','0']
3ô # Split it into chunks of length 3
# i.e. ['0','3','8','9','1','0'] → [['0','3','8'],['9','1','0']]
O # Sum the digits in both parts
# i.e. [['0','3','8'],['9','1','0']] → [11,10]
Ë # Check if they are equal (if they are, they remain in the filtered list)
# i.e. [11,10] → 0
EDIT: Seems I (and most other answers) slightly misread the challenge and the amount of numbers is being asked instead of the numbers themselves within the range. In that case a trailing }g can be added (close the filter; and get the amount of numbers left in the filtered list), so it's 10 13 bytes instead:
Ÿʒ₄n+¦S3ôOË}g
