As correctly pointed out in the comments: The term is asymmetric cryptography, also known as public-key cryptography.
###How do we know that it's asymmetric encryption?###
In symmetric encryption the encryption key and decryption key are identical, meaning you can decrypt data with the same key that it has been encrypted with.
On the other hand, in asymmetric encryption the encryption key and decryption key are different from one another ($K_{Enc} \ne K_{Dec}$) and in your example it's stated:
The encrypted data cannot be decrypted with key $E$.
###How to create $E$ from $D$###
This can be achieved with the following procedure:
Create a key $K$ with a key derivation function by using your password. You can think of this function as a key-stretching-function. KDFs can be used to stretch keys into longer keys or to obtain keys of a required format. This is important to get an input which is "random enough" for step 2.
You can now use this created key $K$ as a seed for a PRNG (pseudo random number generator). Important here is the word pseudo, which means that given the same seed it will always return the same created number.
The PRNG is used for a key-pair-generation-algorithm, which then returns the public-key $K_{Public}$ (in your example $E$ for encryption) and the private-key $K_{Private}$ (in your example $D$ for decryption).
You can now use this generated keys for any asymmetric cryptography methods, some well known examples are:
- ECDH (Elliptic-Curve-Diffie-Hellman).
- RSA
Important: I left out that you would have to use different key-pair-generation-algorithms, depending on which asymmetric cryptographic scheme you would use.