Show data in a database that occurred before a date in another database

Question

I am trying to figure out the time between the day an order being placed and the day the user received an email before they placed an order.

There are currently two databases I am working with, one that has USER_ID and ORDER_DATE and one that shows USER_ID and EMAIL_DATE . I am trying to find the time between most recent order and most recent email received before their order, though users can also receive an email after they placed an order.

What I have tried so far is

SELECT o.USER_ID, MAX(o.ORDER_DATE), MAX(e.EMAIL_DATE)
FROM ORDERS AS o, EMAILS AS e:
INNER JOIN e ON o.USER_ID = e.USER_ID
GROUP BY o.USER_ID

This is getting me the most recent ORDER_DATE and most recent EMAIL_DATE for each user, but I only want to see the most recent email that occurred before the ORDER_DATE and I am at a loss for how to do it.