How do I sum up values only in cells that are color filled?

This thing drives me crazy for the past few days. Please helpI can go to sleep.
I have several columns with numerical data. When certain criteria are met, a person manually makes some of the column fields a green fill color via the color fill button.

Let's say I have data in cells E4 to E14
Below, I have a total field (auto Sum function used to total all),
And, another row with The Colored Green totals.
How do I enter the appropriate code to total only the fields that are green??
I have found some info on verious sites but I have been unsuccesful to implement.
(http://www.cpearson.com/excel/colors.aspx)
I attach a sample sheet, I was playing around a bit, you can ignore the fill color red, just deal with the green fields.

Thank you in advance for any of your help.