Only by obtaining the plans for Concorde via espionage (and the French DST secret service being very lax). There was a very interesting programme about Koncordski on C4 years ago (Cutting Edge or Secret History I think) which went over it all.
Due to there being no equivalents in Russian measurements to Western standards, they had to approximate and work round problems. The first iteration of the Tu-144 did not have the retractable canards, and by working round problems the Russians had got the wing design - specifically the ogival shape of the wing leading edge - badly wrong. They got it wrong because it did not general the vorticies over the upper surface of the wing at high angles of attack, which Concorde used to lower it's landing speed to levels equivalent to conventional airliners (747 etc.). Because Concorde landed at such a steep angle, the droop-snoot nose was required for pilots to be able to see the runway!
That is not to say that the Tu-144 was not a fine aircraft in it's own right. The retractable canards were a solution to the lack of lift at low speeds and were a original feature which owed no debt to Concorde. Indeed the French employed a Mirage Photo Reconnaisance jet during the Koncordski's display at the 1973 Paris Airshow (which led to the crash of the latter as it took evasive maneuvers to avoid it when it got too close) to study the canards closely, and they were later used on French military jets. The Tu-144 was also larger, faster and had more powerful engines than Concorde.
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