So, what to explain a block after its prior 10-min block is a 38-minute block? Is it a sudden increase of difficulty?
No.
For mining a block, miners need to solve a mathematical problem which is called proof-of work problem.
This problem is solved through brute-force method. This means that the problem is solved by checking all possible answers. It's possible that the problem is solved in a few seconds. It's also possible that it takes more than an hour until a miner finds the solution.
Yup you are definitely right. for every transcation miners need to solve a mathematical problem and everyday million of transcation had been done. that's why need a long time for complete a transcation block. it take more then 10 minutes