I couldn't see any mathematical pattern. So I got the
notion to write out the names for the numbers:

10 = ten       <-- spelled with 3 letters
 4 = four      <-- spelled with 4 letters
60 = sixty     <-- spelled with 5 letters
90 = ninety    <-- spelled with 6 letters 
70 = seventy   <-- spelled with 7 letters
18 = eighteen  <-- spelled with 8 letters

I notice that each one contains one more letter
than the preceding one.  So the next number must
be spelled with 9 letters, since "eighteen" is
spelled with 8 letters.

But I wondered why "1 = one" or "2 = two", or "6 = six", 
which are also spelled with 3 letters, weren't chosen for 
the first number instead of "10 = ten".  So I decided that 
it must be because 10 is the LARGEST whole number whose 
name is spelled with only 3 letters.  

But then that made me wonder why "9 = nine" wasn't chosen
for the second number instead of "4 = four", since 9 is larger
and also spelled with 4 letters.  Then I noticed that all the
numbers are even. So that's explains why "9 = nine" wasn't 
chosen for the second number.  

The pattern is that it's the largest EVEN number that can be spelled 
with that many letters. 

But then I wondered why "70 = seventy" was chosen and not 
"100 = hundred", since both "seventy" and "hundred" have 7 letters.  
And 100 is an even number! Then it occurred to me that the official 
name for 100 is not "hundred" but "one hundred".   

So then I looked for the largest whole EVEN number whose official 
name is spelled with 9 letters.  I came up with "ninety-six",
as the largest even number spelled with 9 letters. I assume the 
hyphen doesn't count as a letter.

So my answer is that the next number is 96.

10 = ten        <-- largest even number spelled with 3 letters
 4 = four       <-- largest even number spelled with 4 letters
60 = sixty      <-- largest even number spelled with 5 letters
90 = ninety     <-- largest even number spelled with 6 letters 
70 = seventy    <-- largest even number spelled with 7 letters
18 = eighteen   <-- largest even number spelled with 8 letters
96 = ninety-six <-- largest even number spelled with 9 letters

Edwin