Is X+Y sorting problem still an open problem?
Here the problem status is "open". The page was revised in 2006 and it seems updated to September 2017, so we can safely suppose that the problem is still open.
Anyway, an algorithm that solves the problem using $O(n^2)$ comparison (and total complexity $O(n^2\cdot \log(n))$) is known from 1992: J.-L. Lambert, Sorting the sums $x_i+y_j$ in $O(n^2)$ comparisons, Theoretical Computer Science, (1992):103, 137–141 doi 10.1016/0304-3975(92)90089-X.