Leverage an Automated System for the emails
Various issue tracking software can be configured to automatically send emails to people. Any time your manager gives you a task, create a ticket for the task in the system. If configured correctly, the system would then proceed to send an automated email detailing everything to you, your manager, and anyone else you want.
If he complains about the automated email, you can shift the blame to the issue tracking software and say it is built in. At the same time, the issue tracking system will provide a nice paper trail of what work you are doing and who requested it.
Even for work that does not involve programming, having a system that tracks tasks is very beneficial. So if you're working in an environment that does not have it, I recommend finding one that meets your needs and act as a champion for its adoption. If used correctly, it can help address the issue you are facing.
