I am not so sure you will be able to find a formula solution; so here is a UDF (user defined function) that you can turn to if it turns out that I am right...
Function SumNums(Rng As Range) As Double
Dim Cell As Range
For Each Cell In Rng
SumNums = SumNums + Val(Mid(Cell.Value, _
Evaluate("MIN(FIND({0,1,2,3,4,5,6,7,8,9}," & _
Cell.Address & "&""0123456789""))")))
Next
End Function
HOW TO INSTALL UDFs
If you are new to UDFs, they are easy to install and use. To install it, simply press ALT+F11 to go into the VB editor and, once there, click Insert/Module on its menu bar, then copy/paste the above code into the code window that just opened up. That's it.... you are done. You can now use SumNums just like it was a built-in Excel function. Now just pass in the range whose cells you want to examine; for example...
=SumNums(B4:C8)
If you are using XL2007 or above, make sure you save your file as an "Excel Macro-Enabled Workbook (*.xlsm) and answer the "do you want to enable macros" question as "yes" or "OK" (depending on the button label for your version of Excel) the next time you open your workbook.