My thinking with mobile push notifications would be you tap the notification and it takes you straight to a simple UI where you punch in the values.

It might be harder to reduce the friction as low as this with email notifications but it could work just as well. A simple link could work, or one step further is having a feature where you can specify expenditure and tags in the reply to an email in a certain format that's parsed by your app e.g:

$8, work, commuting $4.50, lunch

(Values in example may seem low because I'm British but dollar/pound symbol is neither here nor there in this case!)