The short answer is that you can't. Like other answers mentioned you need to assume a fixed effect size, fixed significance level and a desired statistical power in order to estimate the needed sample size.
Now if you don't know the mean difference and standard deviation - you can guess them based on some information.
And if you cannot reasonably do that then the next best thing is to calculate required sample sizes for a whole range of possible mean differences and standard deviations. This would allow you to at least imply on a range of possibilities. And you would be able to answer questions such as "what kind of effects can I reasonably (i.e. with power = 80%) expect to detect with a sample size of n".