Water pressure pump

Hi, I have a water pressure pump that keeps going on every 10 seconds or so to pump the water from the tank to my shower for example. Problem is, every time it turns on, the water pressure increases I'm assuming due to the power surge . This makes taking a shower a very annoying experience as the water temperature fluctuates from a hot shower to freezing cold every time the pump starts.
Did anyone have a similar issue, and what can I do to fix this?
Thank you.

Pressure tank should resolve it.

I think you can run a pipe from the outlet side of the pump back to the inlet side. (A "T" on each pipe.)
I think that way it doesn't repond to back pressure and turn off.