The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

CREATE INDEX dane_all_idx_identyfikator ON DANE_BUD_ALL_BR (Identyfikator);
CREATE INDEX ewidencje_idx_e_numerprojektu ON Ewidencje (E_numerProjektu);

The optimized query:

SELECT
        DANE_BUD_ALL_BR.ID_ewidencji 
    FROM
        DANE_BUD_ALL_BR 
    WHERE
        DANE_BUD_ALL_BR.Identyfikator IN (
            SELECT
                b.Identyfikator 
            FROM
                DANE_BUD_ALL_BR b 
            INNER JOIN
                Ewidencje e 
                    ON e.E_numerProjektu = b.numerProjektu 
            WHERE
                e.E_numerProjektu LIKE b.numerProjektu
        )