Delete lines from a text file that match multiple regexes on a text file

It is a bit messy with sed but possible:

sed -n '
:start
/^\[/{
    h
  :loop
    n
    /^\[/b start
    /^$/b loop
    x;p;g
}
p'

-n means print nothing by default. :start is just a label for a later goto. We match lines beginning [ and start a group ({...}) of commands. We copy the line to the hold space (h). We get the next line (n). If it begins [ we had an empty section, so goto (b) the start again.

If the line is empty (/^$/) we read another line (goto loop). The line is not empty so we exchange the line with the held section header (x), print the section header (p), get the current line back (g) and continue out of the group of commands to print (p) the line. This last (p) also prints non-section headers.

To extract lines containing only digits:

$ grep -x '[0-9][0-9]*' words >digits

The regular expression [0-9][0-9]* will match any line contains at least one digit, and the -x option to grep requires that the whole line matches the given expression.

If your file doesn't have empty lines, you may change it to grep -x '[0-9]*'.

If you want lines with numbers, delete lines with alphabetic characters instead (easier than trying to construct a regular expression for a generic number):

$ grep -v '[a-zA-Z]' words >numbers

Both variants using POSIX character classes:

$ grep -x '[[:digit:]][[:digit:]]*' words >digits
$ grep -v '[[:alpha:]]' words >numbers

Update: If you want to select the lines containing floating point numbers you could use the (extended) regular expression ^[+-]?([0-9]*\.)?[0-9]+$:

$ grep -x -E '[+-]?([0-9]*\.)?[0-9]+' words >floats

It all comes down to what kind of "number" we're looking for.