Creating a table with CHECK constraints in MySql workbench
This can be done very elegantly using CHECK constraints in MySQL &gt;=  8.0.16 as follows (fiddle available here):
Your table (changed slightly)
CREATE TABLE IF NOT EXISTS orders 
(
  order_no INT,
  order_type CHAR(8) CHECK (order_type IN ('e', 'i')) ,
  engine_description VARCHAR(45) DEFAULT 'The default',  -- NOT NULL constraint removed
  CONSTRAINT ot_ed_ck 
    CHECK ((order_type = 'i') OR (order_type = 'e' AND engine_description IS NULL))
);

Populate it:
INSERT INTO orders 
VALUES 
(1, 'i', 'safadf'), (2, 'i', 'xcvzxv'), (3, 'e', NULL);

Then
SELECT * FROM orders;

Result:
order_no    order_type  engine_description
       1             i              safadf
       2             i              xcvzxv
       3             e                null  

So far, so good.
Then we try to do this:
INSERT INTO orders VALUES ('4', 'e', 'xxxxx');

and we get the error message:
Check constraint 'ot_ed_ck' is violated.

Which is exactly what we want!
To cover the case of or else a value will be added? in the question, by which I presume you mean a DEFAULT - if we specifically exclude engine_description from the list of values to be INSERTed as follows:
INSERT INTO orders (order_no, order_type) VALUES (5, 'i');

and we SELECT:
SELECT * FROM orders

We obtain:
order_no    order_type  engine_description
      1              i              safadf
      2              i              xcvzxv
      3              e                null  
      5              i         The default   &lt;&lt;----- Default!

I would strongly urge you to upgrade to MySQL 8 - it's now at version 8.0.22, so any major version change wrinkles will have been ironed out by now - you get all sorts of goodies - like CHECK constraints that I just outlined, COMMON TABLE EXPRESSIONs (available from 8.0.1, aka the WITH clause) and also GENERATED columns (5.7.5).
If you cannot upgrade to version 8, then you'll have to use TRIGGERs (as per @nbk's answer), but you asked for constraints so that's what I supplied.
Also, what exactly do you mean by:

Also, if I want to do the same for two different entities?

If you mean constraints between two fields in the same table (intra-table), you have the example above, if you mean between two tables (inter-table), then on any server (bar Firebird), you'll have to use TRIGGERs!
Finally, a word of advice - do NOT use SQL keywords as table or column names (in this case Order)- it's confusing, makes debugging more difficult and is not good practice.  Normally, I use singular table names, but I make an exception (obviously) for ORDERs - a table is a set and should be singular (IMHO).
p.s. welcome to the forum!