diff says memory exhausted need help with perl

I've got two similar large files with one word per line and they're
sorted.
Each file has a few words not in the other.
I typically identify the unique words in the file using diff,grep,cut.
When the files are too big (2Gig) diff dies with "memory exhausted".

I want to search for the unique words in file1 but I might need to
ping-pong since neither file is a superset of the other.
I don't want to be limited by physical RAM as the file sizes exceed
RAM.

I assume I'm not the first to have this problem.
Can someone point me to perl code?
TIA

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