A simple hand with Java Pattern Matching?

I have had a good go at using Java OpenJDK, necessarily a very early version of the OpenJDK, in order to try and match expressions like the following, which are going to be certain kinds of doubles in exponential, E, notation:

Code:

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import java.util.regex.Pattern;
import java.util.regex.Matcher;
import static java.lang.System.*;

//...

Pattern pattern = Pattern.compile("^[0-9]+\\.0{15}?|9{15}?[0-9]+E-?[0-9]+$");
     
Matcher matcher = pattern.matcher("3.0E-4");
     
boolean result = matcher.matches();

out.println("Pattern match result: " + result + ".");

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I want to anchor to the left, have any number of integers 0-9, specify a decimal point . , then have either 15 zeroes or 15 nines, any one digit 0-9, the letter E, possibly a negative sign, 3 integers 0-9 and then anchor to the right.

How do I update my regular expression pattern above, so that it will match Strings like "3.0E-4" and come back true
with Strings like this, and more broadly, if you gather my intentions with what I wish to be matching to?