By 'existing page' do you mean a WordPress page? My experience with rewrites is routing everything to index.php with whatever extra query vars you need, I think attempting to route it to `edit` is one of your issues, not entirely clear on your intent there.

Go download [Monkeyman Rewrite Analyzer](http://wordpress.org/extend/plugins/monkeyman-rewrite-analyzer/) if you don't already have it, it's a great tool for testing these things out.

I tested out the following rule to verify it works. All requests to `/edit/*` load a page named 'edit', `get_query_var('e')` returns the correct value for `e` in my template.

Note I didn't flush the rules here, I usually just visit the `Settings > Permalinks` page and click save to flush whenever I change them.

    <?php
	
	add_action( 'init', 'my_rewrites_init' );
	function my_rewrites_init(){
		add_rewrite_rule(
			'edit/([^/]+)/?',
			'index.php?pagename=edit&e=$matches[1]',
			'top' );
	}
	
	add_filter( 'query_vars', 'my_query_vars' );
	function my_query_vars( $query_vars ){
		$query_vars[] = 'e';
		return $query_vars;
	}