This SEDE query does the job:
It returns Why is it faster to process a sorted array than an unsorted array? as the highest scoring java question, and the highest scoring java answer is also on this question (but that could be different).
For reference, here is the complete query (it could probably be written in a more efficient way, but it's just an adaptation of this query):
QuestionID AS [Post Link], q_.OwnerUserId AS [User Link], q_.Score AS [Q score],
AnswerID AS [Post Link], a_.OwnerUserId AS [User Link], a_.Score AS [A score]
(SELECT TOP 1 q.Id
FROM Posts AS q INNER JOIN PostTags AS qt ON q.Id = qt.PostId
WHERE qt.TagId = t.Id ORDER BY q.Score DESC) AS QuestionID,
(SELECT TOP 1 a.Id
FROM Posts AS a INNER JOIN PostTags AS at ON a.ParentId = at.PostId
WHERE at.TagId = t.Id ORDER BY a.Score DESC) AS AnswerID
FROM Tags AS t
WHERE t.TagName = ##TagName:string##) AS temp
INNER JOIN Posts AS q_ ON temp.QuestionId = q_.Id
LEFT OUTER JOIN Posts AS a_ ON temp.AnswerId = a_.Id
Note that SEDE is updated once a week, on Sunday morning, so the post scores could be a little bit off.