I need to switch back on my new phone to my old email I don’t know how to do it

Did you restore your new iPhone from the backup of the old one?

If yes, your Mail account should also be restored.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

In any other case set the Mail account up again, as explained in this article:

Add an email account to your iPhone, iPad, or iPod touch - Apple Support

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. If possible, also set up Family Sharing  between the IDs to keep access to your apps/purchases. 

 How to switch Apple IDs on your iPhone or iPad.      

 What to do after you change your Apple ID or password - Apple Support.    

How to transfer all files from one iCloud account to another.    

Family Sharing.         

Family Sharing - Set up.