Question: Could you explain the difference between 'after 10 months' and 'in 10 months'?

Well, as a preposition of time, 'in' here means talking about a period of time, ten months, no more, no less than that time. The actual meaning of this phrase 'in ten months' is 'within ten months'.
这里的in意思就是"在某段时间之后",不多不少.

Here are some examples of things that will occur within the set period of time indicated by 'in ten months':
In ten months, I'll be 30 years old.
(This sentence means ten months in the future from now, not more than that.)
They'll have travelled through 20 different countries in two continents in ten months.

So what about the expression 'after ten months'? Well this usually means in 11 months or more. This phrase implies ten months have to pass ahead of the time of speaking and it's any time after those months have passed that we are referring to. Here are some examples to clarify:
I'll change jobs after ten months here.
After ten months, I won't need to take any more medication.
"after ten month"指过了10个月后的任意一个时间点。

'After ten months' can refer to future time, like in the examples I just gave you, or refer to past time like this:
She studied Spanish twice a week at evening class and, after ten months, she could speak fluently.
Although 'in ten months' usually refers to an event that will happen ten months from now, it can also be used in the past. An example is:
I learnt to drive and passed my test in ten months - which means driving was learnt within a ten month time frame. But personally, I learnt to drive in three months.

大家弄清楚in ten month和after ten month之间的区别了吗？我们再看看其它的例子。

she learnt to drive in three weeks.
她花了三个星期就学会了开车。

这句话还可以表达为: After three weeks she could drive.