They are pretty much the same when 'so' refers to 'very much' as a adv, but, there is a slight difference. As you know 那means that, 这means this, so, it's pretty much the the problem of 'this or that'. Before I give you some examples that will help you understand them better, remember, they are spoken Chinese, not written or formal language. People use them to show that the situation is a little unexpected, surprised etc. Two students were talking in the classroom, A: Do you know Professor Lee gave Class C a very difficult test that nearly half of the students failed? B: wow...so difficult那么难啊！（Notice: They are talking about other students' test, not theirs, so it's a 'that'.） Few days later, Professor Lee gave them the same test. A and B finally saw the difficult test they heard of in person, and they said simultaneously: wow...so difficult 这么难啊！ (Notice: Now the test has become the problem of their own, so it's a 'this'.) e.g. A: Mike and Cathy only met three months ago, but they're now engaged. B:So soon.那么快！(Because it's about Mike and Cathy, nothing to do with B, it's a 'that'.) The question I posted two minutes ago already got five answers. So soon! 这么快(Because it's yours, it's a 'this') When 'so' as a conjunction, meaning therefore, hence, etc. then it is definitely那么. 这么has no such usage. e.g. The taxi is waiting downstairs, so(那么) let's get going. I'm no scholar and I don't like grammars at all, I'll just give you more lively examples to help you understand. e.g. 1. A: I tasted Pecking duck when I was in Beijing. B: Is it really so (那么) delicious as they say? 2. A: Hi, you also live on this street? B: Yes, I didn't know our flats are so (这么)close. See? And, when it's just 'very', no 'this' or 'that' involved, then don't bother use '这么'or'那么'，adverbs like '很'、'非常' etc are fairly enough. e.g. As every student says, Professor Lee's test is so(非常) difficult.

"这么"谈及的应该是当前的,现在的，比如：你回来的怎么这么快？（表示他刚回到你面前，刚刚发生的事情） "那么"谈及的应该是过去的,久远的，比如，别人叙述完一件事情，你说，是那么回事啊。 “那么多问题”这里，那么和这么可以换用，“那么多问题”，表示你还有解决的时间。或者，只是叙述一件事情。“这么多问题”，表示问题就在你眼前，没有很多时间解决。或者，表示是和自己有关系的问题。 不管怎么解释，必须要对照上下文理解。Anyway,you should try to understand according to text.

那么：1.like that；in that way.问题没有他所想象的那么复杂。The problem is not as complicated as he imagined. 2.about；or so 再有那么五六元钱就够了。Another five or six yuan will probably be enough. 3.then；in that case .既然这样不行那么你打算怎么办呢？Now that it did not work， then，what do you think? 这么：so；such；this way；like this 应当这么做。 It should be done this way. 大家都这么说。 So they say.

Let me tell to you if you want use they in font of one Adjective ,then always USE "这么",No Use "那么",Although sometimes they can be interchanged . When you use the "那么",look the word. 天晴了，那么，出发吧 Are you see? Here the "那么" is Totally different with the "这么"

【这么】zhème 1）[so]∶指示程度、方式、性质等 这口井这么深啊! 2）[like that]∶那样的 这张桌子原来就这么放的。 3）[this way]∶这样 这个句子应该这么翻译。 【那么】nàme [that] 1）用来形容事物性质、程度 你别那么生气。 2）泛指行为和动作。常和“这么”配合使用） 不准这么,不准那么,谁要犯了,就得受处罚