I'm sure you can clean this up but it will do what you want.

; with cte

as

(select d.idxmrn, d.dischargedate, a.apptdt2, DATEDIFF(d,d.dischargedate, a.apptdt2) daysSince, ROW_NUMBER() over (PARTITION by d.idxmrn order by d.idxmrn,DATEDIFF(d,d.dischargedate, a.apptdt2)) as rownum

from discharges d

inner join appointments a

on d.idxmrn = a.idxmrn

group by d.idxmrn, d.dischargedate, a.apptdt2

having MAX(d.dischargedate)<MIN(a.apptdt2)

)

select * from cte where rownum = 1