Internet Explorer hides the clock, forcing me to jump out of the application in order to see what the time is.
Is there a way to force the clock (and other icons to show) while browsing?
You can temporarly show the clock by pressing and hold back button. It will bring the fast app switch where you can see the clock.
In portrait mode, the system tray (including the clock) will show while either the SIP/keyboard is visible or the menu is expanded. I'm not aware of any way to show the system tray all the time.
It's not possible to show the clock at all in landscape mode.
I would go with Richards answer. Just press the three dots at the right bottom corner and the clock will appear.
A quick tip that I use myself is to just start dragging the three dots, as soon as you start moving them the clock will appear. That way you can quickly show the clock without hiding the webpage itself :)