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.

Thank you for your links, I tried the 3rd one, just copied and pasted the code, changed the ranges etc, but can't get it work.
I appreciate your help, if it is not too time consuming it would be great if you opened my sample sheet and provided the code to total one of the green columns so I can see 1st hand. Thank you!!! you will really take my headache away.

Thanks so much VBA Noob.. I think I can rest 90% now. Here is the 10%.
Is there a way to automatically update the totals, if I go back after the function entry and make another field green?
When I change a new field in an old column the sub-total does not update unless I click on the field and press return. Can the update happen automatically when I make a new field green?
Thanks so much!!

Thanks again VBA Noob.
What is the correct procedure to enter the application.volatile code?
I appreciate your help, you really made my day!

Thanks VBA Noob, I ended up using an extra "update" button with a macro attached to update fields, this will work.
Q. Did you enter the extra modules in my original excel sheet attached, or, were they added by me while experimenting (going crazy), to make this work?
Or, did you just add the fomula's in the subtotal fields?I think in one of my tries, when I deleted the extra modules in the excel sheet, even with your formula's in the subtotal fields, I got the ?NAME in the subtotal, so I left them alone.
THANKS AGAIN FOR YOUR SUPPORT, YOU ARE ABSOLUTELY AWSOME!!! Your gesture and quick help makes this world be a better place.

Thanks for everything! Best Wishes, John