This will do it:

function edit_screen_title() {
    global $post, $title, $action, $current_screen;

    if( isset( $current_screen->post_type ) && $current_screen->post_type == \'post\' && $action == \'edit\' )
        $title = \'Edit \' . $post->post_title;
}

add_action( \'admin_head\', \'edit_screen_title\' );