Calculating type I error on the basis of Null-hypothesis: true count differs by 10%

Mosses grow as cell filaments when they are young (just a little like algae).

In this biological example, I am concerned with a mutant moss line that we hypothesized to have a higher cell count in moss filaments. I could not find evidence for a difference, though. A Null-hypothesis, using the t-test had to be maintained.
Now, I wonder how I would do statistical calculations with the Null-hypothesis of a set difference of for example a 10% difference. I want to know how valid my experiment is to support a zero difference is. To what percentage would my experiment with a given sample size and variation show a difference of 10% between populations as significant and how could I practically calculate this.
Usually one establishes a zero-difference Null-hypothesis, that one wants to reject.
Now I want to establish a 10%-difference Null-hypothesis, that I want to reject.
help me please. :)
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Not a robit
So you have two samples you want to compare. And the hypothesis isn't a two-tailed null but a 10% difference. This sounds like a superiority test, which is one-sided and has a margin (e.g., 10%). Look up superiority tests if you have two samples. Also, if you have counts, what do these count values look like, an approximate normal distribution may be alright, or you may need to look at count models - such as Poisson.