I agree that it cant be done with the estimate equation.
I was really fishing for alternative approaches (bootstrap methods, chi squared approximation, etc)
Actually I have one other peice of information ... the parent population is exponentially distributed ... therefore the standard deviation is equal to the mean. So would this mean that the standard error is equal to the mean?
I would highly doubt any method that purports to allow estimation of anything remotely resembling a standard deviation, variance, or mean, with just one data point....a bunch of junk, IMHO.
Yes, you could then infer the standard deviation, but not the standard error of the mean would still be s/sqrt(n) - I guess in this case you could hazard a guess by using s and picking a hypothetical sample size....