Range of five-digit numbers with distinct digit-pair sums

Call a five-digit integer good if no two different pairs of its digits have the same sum (for example, the three-digit $174$ would qualify). If $x$ and $y$ are the smallest and largest good five-digit integers, what is $y-x$?

88505. Build greedily. Largest: $9,8,7$ are fine, $6$ fails ($6+9=7+8$), $5$ works, then $4$ and $3$ fail and $2$ works, so $y=98752$. Smallest: $1,0,2$, then $3$ fails, $4$ works, $5$ and $6$ fail, $7$ works, so $x=10247$ and $y-x=88505$.