Something like:
SELECT t1.Number, t1.DateOfBirth
,COALESCE(t1.PreOpOrg, t2.PreOpOrg) AS PreOpOrg
,COALESCE(t1.PreOpModality, t2.PreOpModality) AS PreOpModality
,COALESCE(t2.PostOpOrg, t1.PostOpOrg) AS PostOpOrg
,COALESCE(t2.PostOpModality, t1.PostOpModality) AS PostOpModality
,t1.DiagDate
FROM t1
JOIN t2
ON t1.Number = t2.Number
UNION ALL
SELECT Number, DateOfBirth, PreOpOrg, PreOpModality, PostOpOrg, PostOpModality, DiagDate
FROM t2
WHERE NOT EXISTS
(
SELECT 1
FROM t1
WHERE t1.Number = t2.Number
)