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阳光总在风雨后

通过 / 经过

tōngguò / jīngguò

Similarities

Both can mean “through”, “thanks to”.

(Tōng)(guò)()(jiā)(de)()()(gōng)()(shēng)(yi)(yuè)(zuò)(yuè)()
Through everyone's efforts the company's business grew and grew.
(Jīng)(guò)()(jiā)(de)()()(gōng)()(shēng)(yi)(yuè)(zuò)(yuè)()
After everyone's efforts the company's business grew and grew.
Either word works in this sentence.

1. Method or process?

通过 stresses the METHOD: what the result was achieved by. 经过 stresses the PROCESS: what was gone through.

()(wàng)(tōng)(guò)(zhè)()(huó)(dòng)(yǐn)()()(jiā)(de)(xìng)()
We hope to arouse everyone's interest through this event.
(Jīng)(guò)()()()(shī)(bài)(zhī)(hòu)()(zhōng)()(chéng)(gōng)(le)
After going through failure upon failure, he finally succeeded.

2. Going past a place

通过 — to enter one side and come out the other. 经过 — to go past, to go by way of; you needn't cross it at all.

(Zhè)()(zhèng)(zài)(xiū)()()(chē)()()(tōng)(guò)
The road here is under repair; cars cannot get through.
()(zhèng)(hǎo)(jīng)(guò)这儿(zhèr)(shùn)便(biàn)(guò)(lái)(kàn)(kan)()
I happened to be passing by, so I dropped in to see you.
()(měi)(tiān)(jīng)(guò)()(ge)(gōng)(yuán)
I go past that park every day.

3. 经过 can also be a noun

(Xiǎo)(Wáng)()(shì)(qing)(de)(jīng)(guò)(gào)(su)()(le)
Xiao Wang told me the whole course of events.
As a noun 经过 means “the course of events”, “what happened”. 通过 is never used this way. ❌

Both in one sentence

(Jīng)(guò)()(nián)(de)(xué)()()(zhōng)()(tōng)(guò)(le)(kǎo)(shì)
After a year of study I finally passed the exam.
经过一年的学习 — what was gone through (the process). 通过了考试 — what was achieved (the result). That is the easiest way to hold the difference in mind.
通过经过
Method, meansProcess, experience
Cross from one side to the otherGo past or by way of
Pass an exam or interviewNot used in this sense
Never a nounCan be a noun: “the course of events”
Remember: 经过 — what you went through. 通过 — how you achieved it, or what you passed.