Here's a picture.
The top distribution represents your H0 hypthothesis.
The bottom distribution represents your H1 hypothesis.
With your effect size, I presume you mean a Cohen's d?
If that is the case, the picture represents your problem properly: the 2 mountains are apart by a distance which is the standard deviation.
To get a power of 95%, your beta must be 5%.
You would also have an alpha of 5%.
To get alpha and beta both 5%, your need mountains that are narrower - so narrow that the situation becomes symmetric.
It means that the area where alpha begins needs to be 1.96 SE from the mean of the left mountain.
And it also means that the area where beta ends needs to bee 1.96 SE from the mean of the right mountain.
In other words, the distance of the mountains (which is sigma), needs to be 2 x 1.96 SE.
In an equation:
Can you solve that for n?