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I want to indent only the first line of each paragraph (as old fashioned as this may be).

It sounds like you need a word-processor not a text editor but, seeing as you ask, do a find and "replace all"
Search for
\n[^\t]
Replace with
\n\t
with "Regular Expression" box ticked
Go to the start of the file (Ctrl-Home) and put a tab there if there is not one.

This is quite over my head but I shall try my best.
Thank you!

Search for
\n[^\t]
Replace with
\n\t

Not a good idea - it looses the first character.
Better:
search for replace by

oops! You're right Andreas