In one case, you want the replacement expression to be a Perl expression,
In the other, you want the value of $1 to be evaluated. 

# s/(10)/$1+1/e
$dollar1 = "10";
$replace = $dollar1 + 1;   # One 'e', so Perl expression.
print $replace;            # 11

# s/(10\+4)/$1/e
$dollar1 = "10+4";
$replace = $dollar1;       # One 'e', so Perl expression.
print $replace;            # 10+4

# s/(10\+4)/$1/ee
$dollar1 = "10+4";
$replace = eval $dollar1;  # Two 'e', so Perl expression + eval.
print $replace;            # 14

[download]

Update: Oops, this was supposed to be a reply to Re^2: /e in regexes.

In reply to Re^3: /e in regexes by ikegami
in thread /e in regexes by waldner

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.