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You can use the query below:

DECLARE @Sentence VARCHAR(MAX) = 'The quick brown fox jumps over the lazy dog' 

DECLARE @first_space_index int = CHARINDEX(' ', @Sentence) - 1
DECLARE @last_space_index int = CHARINDEX(' ', REVERSE(@Sentence)) - 1

IF @first_space_index < 0
	SELECT @Sentence AS [First Word], @Sentence AS [Last Word] 
ELSE
	SELECT SUBSTRING(@Sentence, 1, @first_space_index) AS [First Word], REVERSE(SUBSTRING(REVERSE(@Sentence), 1, @last_space_index)) AS [Last Word]

First Word   Last Word
------------ -----------
The          dog


If @Sentence = 'The' then the result will be:

First Word   Last Word
------------ -----------
The          The