An alternative to Luis' method:
SELECT
e.*,
x.Addresscode, x.AddressType, x.[Address]
FROM #employee e
OUTER APPLY (
SELECT TOP 1 *
FROM #EmpAddress a
WHERE a.Eid = e.Eid
ORDER BY AddressType, Addresscode
) x
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