Stringing together formula in Excel to create one formula that looks at multiple factors

Hi, 

I am trying to write a formula that returns a YES or NO in one cell, based on several different sets of criteria for values in 2 other cells. 

I know how to write the formula for each different set of criteria, but i cannot work out how to string them all together so that all are considered for the YES/NO result. 

I have tried multiple ways of putting them together and it's just going way over my head and past my formula knowledge so would really appreciate some help in how to do it. (I've never managed to get my head around more complex OR functions which is what i think is needed here?) 

I have listed the separate formulas below: 

=AND(D10>=1, D10<=31, E10="Days NET") – YES

or

=AND(D10<=30, E10="Days after receipt") – YES

or

=AND(D10<=30, E10="Days after EOM") – YES

or

=AND(D10>=29, E10="Days after EOM")  - NO

or

=AND(D$0>=29, E10="Days after receipt")  - NO

or

=IF(D10>=30)  - no

In explanation:

If the value in D10=30 AND the value in E10='Days NET',  OR  the value in D10 is less than 30 (regardless of value in E10),  result is YES. 

Or If the value in D10=30 AND the value in E10 is 'Days after EOM' or 'DAYS after receipt', result is NO

If the value in D10 is over 30, result is always NO (regardless of value in E10). 

D10 is an empty cell that can have any 2 digit number entered.

E10 is a drop down list of 3 options only (Days NET, Days after EOM or Days after Receipt)

Result formula is going in cell H10. 

I would really appreciate any guidance on how to create this formula. 

Thanks in advance!