Dell hasn't released any Windows 10 drivers for that model, and their official line is that it doesn't support Windows 10 (they even published a list of compatible models which doesn't include the T3400.
However, yesterday I saw several posts on other forums where T3400 owners were running Windows 10 on it with no problems whatsoever. This is no doubt due in large part to Windows 10's extensive hardware support, either built-in to the OS or via Windows Updates.
So I would go for it, it's the only definitive way to find out.