There are lots of ways to do this. As the others have noted, it wouldn't be common practice to store the reverse or inverted id like this. You can get the display_id several ways. These come to mind quickly:
CREATE TABLE test (entry_id INT)
GO
INSERT INTO test VALUES (1),(2),(3)
GO
--if you trust your entry_id is truly sequential 1 to n you can reverse it for the display_id using a subquery
SELECT entry_id,
(SELECT MAX(entry_id) + 1 FROM test) - entry_id display_id
FROM test
--or a cte
;WITH cte AS (SELECT MAX(entry_id) + 1 max_id FROM test)
SELECT entry_id,
max_id - entry_id display_id
FROM test
CROSS APPLY
cte
--more generally you can generate a row easily since sql server 2005
SELECT entry_id
,ROW_NUMBER() OVER (ORDER BY entry_id DESC) display_id
FROM test
You could use any of those methods in a view to add display id. Normally I'd recommend you just let you presentation layer handle the numbering for display, but if you intend to query back against it you might want to persist it. I can only see storing it if the writes are infrequent relative to reads. You could update a "real" column using a trigger. You could also create a persisted computed column.