I’m not sure why you’re having a problem. For instance I can use the standard WordPress API function the_ID() in my header template – something like this, as an example, and it outputs the ID as expected:
<title> <?php the_ID() ?> </title>
And if I change that to:
<title> <?php the_title() ?> </title>
Then – certainly on single event pages – it output the post (event) title within the page’s title element (and note that I didn’t explicitly pass in the ID).
Does that clarify/help at all?