Here's a solution with a fully worked-out logical path. Blue means "no circle here"
The given circle must have a separation distance of 6 from the other circle in its row (as the black square in its row is (6, 6) so distance of 6 for both row and column).
Either the row or column for the (4, 8) black square must have circles with separation distance 8 - on a 10x10 grid, this mean circles on either edge. If it is the row, then the (1, 2) black square will have separation distance of 0 in its column, a contradiction. Therefore the 8 clue applies to the column of the (4, 8) black square.
For rows/columns with only one circle, color in blue any squares that have a separation distance other than the two allowed distances. (The two allowed distances being the numbers in that row/column's black square)
There is only one way to place circles with separation distance 6 for the (6, 0) black square. Then since the (4, 8) black square already has its 8 clue satisfied, the new circle in its row must have separation distance 4. There is only one way to complete this row now.
There is only one way to place circles 6 apart for the (6, 6) black square's column. We can then trivially complete the (1, 2) black square's clues.
The (7, 4) black square's column only has barely enough space for separation distance 4, and won't fit 7. Using 4 as the column clue and 7 as the row clue allows it to be satisfied.
First trivially completing the row clue for the (6, 0) black square (it must be 0), then notice that there is only one way to fit a separation distance 2 for the (2, 2) black square's row. The (2, 2) black square can be completed.
The rest is trivial deduction.