You've specified a "pattern" to look for in your "e" string, but you've not specified what you want to do when it's found. I'm not certain gsub is suited to your purpose - normally you'd attempt to replace the matching text or run a function based on it (Lua is wondering what to replace with, or run). I suggest taking a closer look at
this string tutorial.
I've not tried it via ComputerCraft (just
repl.it), but this sort of code may be somewhat more suitable:
e="<form action=\"/session\" id=\"login_form\" method=\"post\"><div style=\"margin:0;padding:0;display:inline\"><input name=\"authenticity_token\" type=\"hidden\" value=\"cabbagecabbagecabbage\">"
c,d,e = e:find("value=\"(.*)\">")
print(e)