There is no reason to subtract SDs except for wanting to know how much larger one uncertainty is than the other. If your question is "How to compare u1 +/- SD1 to u2 +/- SD2?' then you must use the method of propagation of error given Jochen. 

The SD is a measure of uncertainty. u1 and u2 are uncertain quantities. If you add or subtract one uncertain quantity from another uncertain quantity, the result must be more uncertain than either of the quantities.

I learned propagation of error from a radiochemistry text. On my book shelf there are 4 well-known statistics texts. I could not find one mention of error propagation in the index of any of them.

I don't really understand your question. The two SDs are just numbers, so they are added or substracted like numbes in the usual (and only) way. But I suppose this is not the intention of your question. I can only guess: is it that you want to estimate the expected SD of the difference between measurements from the two samples? If so, you can get this value from Gaußian error propagation as sqrt( [SD1]² + [SD2]² ).

You can only add and subtract variances - not standard deviations. This is inherent in the reply and formula from Jochen.

 There is no reason to subtract SDs except for wanting to know how much larger one uncertainty is than the other. If your question is "How to compare u1 +/- SD1 to u2 +/- SD2?' then you must use the method of propagation of error given Jochen. 

The SD is a measure of uncertainty. u1 and u2 are uncertain quantities. If you add or subtract one uncertain quantity from another uncertain quantity, the result must be more uncertain than either of the quantities.

I learned propagation of error from a radiochemistry text. On my book shelf there are 4 well-known statistics texts. I could not find one mention of error propagation in the index of any of them.

The standard deviation can't be added itself, unless you first add the variances and then take the square root to get the addded standeard deviation.