After editing to get your HTML snippet out in the open, I think I can start to answer.
First off, PHP and HTML are two entirely different creatures. PHP runs on your server and produces output. HTML is a type of output your PHP can produce, and when running on a web sever, it is the default content type. Most websites (I'd say 99%, if not even 100% given rounding) that use PHP also use HTML.
If you're instead crafting, say, a website that only uses plain text (talk about hard to navigate), you're out of luck. Browsers will automatically look for your favicon at /favicon.ico
, but if you want to also offer an animated GIF, you need to state that using the HTML tag you've given. Nothing else (HTTP headers, etc.) can mimic that effect.
But seriously, if you're not using HTML for your website, what are you using?