If each cell is filled only with numbers and letters, a quick non-vba way to do this is to decompose the substitute function 10 times to remove 10 numeric characters. what you have left is only alpha. Then you can len() alpha text / subtract this number from the original length to get the number length.
Assuming "1234567ABC" is in cell A1:
This formula gives the number of letters. (3)
=LEN(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(A1,0,""),1,""),2,""),3,""),4,""),5,""),6,""),7,""),8,""),9,""))
This formula gives the total number: (7)
=LEN(A1)-LEN(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(A1,0,""),1,""),2,""),3,""),4,""),5,""),6,""),7,""),8,""),9,""))
If you want to start processing the data in other ways / in more detail, you may need a VBA solution.
Note
To fulfill the requirements in the original post, add this suffix to the end of the above formulas:
=x & " Numbers / Letters"
Where x = the above two formulas. this will add text after the calculated number.
Further reading:
The following link points to VBA UDF, which does something similar: http://www.mrexcel.com/forum/excel-questions/16364-how-remove-numbers.html
Additional update (thanks lori_m)
This LOT formula is easier to read / update:
=SUM(LEN(A1)-LEN(SUBSTITUTE(A1,{1,2,3,4,5,6,7,8,9,0},"")))