User blog comment:MemoryAngel/Hashtags and E's?/@comment-28606698-20170928153425

Saying namely about the example in your post

Using Hyper-E Notation:

$$En=10^n$$

$$E10^{11}=10^{10^{11}}$$

$$E10^{11}\#1=10^{10^11}$$

$$E10^{11}\#2=10^{10^{10^11}}$$

$$E10^{11}\#3=10^{10^{10^{10^11}}}$$

and so on up to

$$E10^{11}\#10^{11}=\underbrace{10^{...^{10^{10^{10^{11}}}}}}_{10^{11}+1\quad 10's}+1$$

E10^{11}\#10^{11}\#2=E10^{11}\#(E10^{11}\#10^{11})=underbrace{10^{...^{10^{10^{10^{11}}}}}}_{\underbrace{10^{...^{10^{10^{10^{11}}}}}}_{10^{11}+1\quad 10's}+1