If that's the text in the column, then you're going to have to use substring at some stage.
declare @l_debug varchar(1000)
select @l_debug = 'PersonId="315618" LetterId="43" MailingGroupId="1" EntityId="551723" trackedObjectId="9538" EmailAddress="[email protected]"'
select substring(@l_debug, patindex('%EntityId="%', @l_debug)+ 10, 6)
If you don't know how long EntityID could be, then you'll need to get the patindex of the next double-quote after EntityID="
declare @l_debug varchar(1000), @l_sub varchar(100), @l_index2 numeric
select @l_debug = 'PersonId="315618" LetterId="43" MailingGroupId="1" EntityId="551723" trackedObjectId="9538" EmailAddress="[email protected]"'
select @l_sub = substring(@l_debug, patindex('%EntityId="%', @l_debug)+ 10 /*length of "entityid=""*/, char_length(@l_debug))
select @l_index2 = patindex('%"%', @l_sub)
select substring(@l_debug, patindex('%EntityId="%', @l_debug)+ 10, @l_index2 -1)