Hi Simon
This is simple but somewhat restrictive:
SELECT A.RetailerID, MIN(B.RetailerIDTheirs) AS RetailerIDTheirs
FROM #TableA A
LEFT JOIN #TableB B ON B.RetailerID = A.RetailerID
GROUP BY A.RetailerID
This is less simple but offers more flexibility:
SELECT A.RetailerID, B2.*
FROM #TableA A
LEFT JOIN (SELECT RetailerID, MIN(RetailerIDTheirs) AS RetailerIDTheirs FROM #TableB GROUP BY RetailerID) B ON B.RetailerID = A.RetailerID
LEFT JOIN #TableB B2 ON B2.RetailerID = B.RetailerID AND B2.RetailerIDTheirs = B.RetailerIDTheirs
Both are likely to be more efficient than a correlated subquery.
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden